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Maths
1 Dec 2025
192
3 pages
The document covers Nat 5 Maths trigonometry problems, focusing on calculating the area of trianglesusing various formulas... Show more
This page delves into more complex triangle problems, including proving trigonometric identities and calculating areas of triangles with given side lengths and angles. These problems are typical of those found in Nat 5 Maths Past Papers and require a solid understanding of trigonometry formulas.
Example Prove that cos A = 1/8 in a triangle with sides 5, 4, and 6.
Highlight The cosine rule is essential for solving problems where you know three sides of a triangle and need to find an angle.
The page also includes a problem where students must calculate the area of a triangle given two sides and the sine of an angle. This type of question tests students' ability to apply the area of triangle formulas in various contexts.
The final page covers more advanced trigonometric calculations, including proving trigonometric identities and solving for missing sides in triangles. These problems are excellent practice for students preparing for Nat 5 Maths Past Papers and help reinforce concepts from the Nat 5 formula sheet.
Example Given that sin 30° = 0.5, show that sin A = 0.3 in a triangle with sides 4, 6, and 10.
Highlight This problem demonstrates the application of the sine rule in a more complex scenario, requiring students to think critically about the relationships between angles and sides in a triangle.
The page concludes with a problem where students must calculate the length of a missing side in a triangle, given its area, one side length, and the sine of an angle. This type of question combines multiple concepts from the Nat 5 Maths curriculum, including area of triangle sine rule and basic trigonometric ratios.
This page introduces non-calculator trigonometry problems for Nat 5 Maths. It covers calculating the area of a triangle and finding missing sides using the sine rule. The problems demonstrate practical applications of formulas found in the Nat 5 Maths formula sheet.
Example Calculate the area of triangle ABC where a=12, b=10, and sin C = √3/2.
Highlight The formula A = ½ab sin C is crucial for solving area problems without a calculator.
Vocabulary Sine rule - A formula used to find unknown sides or angles in a triangle when you know one side and two angles, or two sides and one angle opposite one of them.
The page also includes a problem where students must find the length of a missing side using the sine rule. This type of question is common in Nat 5 Maths Past Papers and helps students practice Sin cos formulas non calculator national 5 maths.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
4
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the properties of interior and exterior angles in polygons. Learn how to calculate the sum of interior angles using the formula (n-2) x 180° and understand the relationship between interior and exterior angles. This summary covers triangles, quadrilaterals, pentagons, and hexagons, providing essential insights for geometry students.
MathsExplore key concepts in trigonometry and quadratic functions, including the area of triangles, sine and cosine rules, bearings, and the properties of quadratic graphs. This summary covers essential formulas and problem-solving techniques for evaluating functions and understanding the nature of quadratic equations.
MathsExplore the Sine and Cosine Rules for solving triangles in this comprehensive guide. Learn how to calculate unknown angles and side lengths using the Law of Sines and Law of Cosines, complete with worked examples and practice questions. Ideal for Edexcel and other exam boards.
MathsExplore the fundamental relationships between angles and side lengths in right triangles, including Pythagorean theorem and trigonometric ratios. This summary covers key concepts such as adjacent, opposite, and hypotenuse sides, essential for mastering trigonometry. Ideal for students preparing for exams or needing a quick reference.
MathsExplore the fundamental concepts of trigonometry, including the Pythagorean theorem, definitions of adjacent, opposite, and hypotenuse sides, and key trigonometric ratios (sine, cosine, tangent) for right triangles. This summary is essential for understanding the relationships between angles and side lengths in trigonometry.
MathsExplore the fundamentals of trigonometry, including key concepts like SOH CAH TOA, trigonometric ratios, and how to find missing sides and angles in right triangles. This summary provides step-by-step methods for solving trigonometric problems, making it ideal for students seeking to enhance their understanding of trigonometric functions and calculations.
MathsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The document covers Nat 5 Maths trigonometry problems, focusing on calculating the area of triangles using various formulas and techniques. It includes examples of solving triangle problems using the sine rule, cosine rule, and area of triangle with 3 sides... Show more
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page delves into more complex triangle problems, including proving trigonometric identities and calculating areas of triangles with given side lengths and angles. These problems are typical of those found in Nat 5 Maths Past Papers and require a solid understanding of trigonometry formulas.
Example: Prove that cos A = 1/8 in a triangle with sides 5, 4, and 6.
Highlight: The cosine rule is essential for solving problems where you know three sides of a triangle and need to find an angle.
The page also includes a problem where students must calculate the area of a triangle given two sides and the sine of an angle. This type of question tests students' ability to apply the area of triangle formulas in various contexts.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The final page covers more advanced trigonometric calculations, including proving trigonometric identities and solving for missing sides in triangles. These problems are excellent practice for students preparing for Nat 5 Maths Past Papers and help reinforce concepts from the Nat 5 formula sheet.
Example: Given that sin 30° = 0.5, show that sin A = 0.3 in a triangle with sides 4, 6, and 10.
Highlight: This problem demonstrates the application of the sine rule in a more complex scenario, requiring students to think critically about the relationships between angles and sides in a triangle.
The page concludes with a problem where students must calculate the length of a missing side in a triangle, given its area, one side length, and the sine of an angle. This type of question combines multiple concepts from the Nat 5 Maths curriculum, including area of triangle sine rule and basic trigonometric ratios.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces non-calculator trigonometry problems for Nat 5 Maths. It covers calculating the area of a triangle and finding missing sides using the sine rule. The problems demonstrate practical applications of formulas found in the Nat 5 Maths formula sheet.
Example: Calculate the area of triangle ABC where a=12, b=10, and sin C = √3/2.
Highlight: The formula A = ½ab sin C is crucial for solving area problems without a calculator.
Vocabulary: Sine rule - A formula used to find unknown sides or angles in a triangle when you know one side and two angles, or two sides and one angle opposite one of them.
The page also includes a problem where students must find the length of a missing side using the sine rule. This type of question is common in Nat 5 Maths Past Papers and helps students practice Sin cos formulas non calculator national 5 maths.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
4
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the properties of interior and exterior angles in polygons. Learn how to calculate the sum of interior angles using the formula (n-2) x 180° and understand the relationship between interior and exterior angles. This summary covers triangles, quadrilaterals, pentagons, and hexagons, providing essential insights for geometry students.
MathsExplore key concepts in trigonometry and quadratic functions, including the area of triangles, sine and cosine rules, bearings, and the properties of quadratic graphs. This summary covers essential formulas and problem-solving techniques for evaluating functions and understanding the nature of quadratic equations.
MathsExplore the Sine and Cosine Rules for solving triangles in this comprehensive guide. Learn how to calculate unknown angles and side lengths using the Law of Sines and Law of Cosines, complete with worked examples and practice questions. Ideal for Edexcel and other exam boards.
MathsExplore the fundamental relationships between angles and side lengths in right triangles, including Pythagorean theorem and trigonometric ratios. This summary covers key concepts such as adjacent, opposite, and hypotenuse sides, essential for mastering trigonometry. Ideal for students preparing for exams or needing a quick reference.
MathsExplore the fundamental concepts of trigonometry, including the Pythagorean theorem, definitions of adjacent, opposite, and hypotenuse sides, and key trigonometric ratios (sine, cosine, tangent) for right triangles. This summary is essential for understanding the relationships between angles and side lengths in trigonometry.
MathsExplore the fundamentals of trigonometry, including key concepts like SOH CAH TOA, trigonometric ratios, and how to find missing sides and angles in right triangles. This summary provides step-by-step methods for solving trigonometric problems, making it ideal for students seeking to enhance their understanding of trigonometric functions and calculations.
MathsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
