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Sin and Cos rules
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6 Jul 2025
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Fun with Sine and Cosine Rules: Questions and Answers PDF for Kids!
The Sine Rule
This page focuses on the application of the Sine Rule, which is used when we know two sides and one angle or when we know two angles and one side of a triangle.
Sine and cosine rule formula: a/sin A = b/sin B = c/sin C
The page provides several examples of how to use sine rule to find angle and side lengths:
- Finding the size of angle R in a triangle with sides 9cm and 3cm, and an angle of 75°. Example: Using the Sine Rule, we get: 9/sin 75° = 3/sin R sin R = / 9 R = sin⁻¹ ≈ 25.4°
- Finding the length of side x in a triangle with a side of 4cm, and angles of 40° and 45°. Example: Applying the Sine Rule: x/sin 45° = 4/sin 40° x = / sin 40° x ≈ 4.46cm
The page also highlights an important property of the Sine Rule:
Highlight: When rearranging the Sine Rule, remember to "change side, change operation." This means if you move a term to the other side of the equation, you need to switch between multiplication and division.
These examples demonstrate the versatility of the Sine Rule in solving various triangle problems, making it a crucial tool for students studying trigonometry.
The Cosine Rule
This page delves into the Cosine Rule, which is used in two specific scenarios: when given two sides and their included angle, or when all three sides of a triangle are known.
Cosine rule formula for side: a² = b² + c² - 2bc cos A
Cosine rule formula for angle: cos A = /
The page provides two key examples:
- Calculating side length with cosine rule example: Find the length of side BC in a triangle where two sides are 7cm and 3cm, with an included angle of 35°. Example: Using the Cosine Rule: a² = 7² + 3² - 2cos a² = 49 + 9 - 34.40 a² = 23.60 a = √23.60 ≈ 4.9cm
- Finding angle using Cosine Rule calculator: Find the size of angle B in a triangle with sides 4cm, 5cm, and 7cm. Example: Applying the Cosine Rule for angles: cos B = / cos B = / 40 cos B = -0.2 B = cos⁻¹ ≈ 101.5°
These examples illustrate how the Cosine Rule can be used to find both sides and angles in triangles, making it a versatile tool in trigonometry. The page emphasizes the importance of choosing the correct formula based on the given information and what needs to be calculated.
Highlight: When using the Cosine Rule, pay attention to whether you're solving for a side or an angle, as the formulas differ slightly.
Understanding when and how to apply the Cosine Rule is crucial for students tackling complex triangle problems in trigonometry and geometry.
Using Sine and Cosine Rules to Find a Side or Angle in a Triangle
This page provides a decision-making guide for choosing between the Sine Rule and Cosine Rule when solving triangle problems. It helps students understand when to use sine and cosine rule based on the given information.
Highlight: The choice between Sine and Cosine Rules depends on what information is given and what needs to be found.
When finding a side:
- Use the Cosine Rule if you know two sides and the included angle.
- Use the Sine Rule if you know two angles and one side.
When finding an angle:
- Use the Cosine Rule if you know all three sides.
- Use the Sine Rule if you know two sides and an angle .
Definition: The Sine Rule is expressed as a/sin A = b/sin B = c/sin C, where lowercase letters represent sides and uppercase letters represent angles.
Definition: The Cosine Rule for finding a side is a² = b² + c² - 2bc cos A, and for finding an angle is cos A = / .
These formulas provide the foundation for solving various triangle problems, making them essential tools in trigonometry.
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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.
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4.9/5
App Store
4.8/5
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
Fun with Sine and Cosine Rules: Questions and Answers PDF for Kids!
The Sine and Cosine Rules are essential tools for solving triangles in trigonometry. These rules allow students to find unknown sides or angles in non-right-angled triangles. This guide provides a comprehensive overview of when and how to use these rules,... Show more
The Sine Rule
This page focuses on the application of the Sine Rule, which is used when we know two sides and one angle or when we know two angles and one side of a triangle.
Sine and cosine rule formula: a/sin A = b/sin B = c/sin C
The page provides several examples of how to use sine rule to find angle and side lengths:
- Finding the size of angle R in a triangle with sides 9cm and 3cm, and an angle of 75°. Example: Using the Sine Rule, we get: 9/sin 75° = 3/sin R sin R = / 9 R = sin⁻¹ ≈ 25.4°
- Finding the length of side x in a triangle with a side of 4cm, and angles of 40° and 45°. Example: Applying the Sine Rule: x/sin 45° = 4/sin 40° x = / sin 40° x ≈ 4.46cm
The page also highlights an important property of the Sine Rule:
Highlight: When rearranging the Sine Rule, remember to "change side, change operation." This means if you move a term to the other side of the equation, you need to switch between multiplication and division.
These examples demonstrate the versatility of the Sine Rule in solving various triangle problems, making it a crucial tool for students studying trigonometry.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The Cosine Rule
This page delves into the Cosine Rule, which is used in two specific scenarios: when given two sides and their included angle, or when all three sides of a triangle are known.
Cosine rule formula for side: a² = b² + c² - 2bc cos A
Cosine rule formula for angle: cos A = /
The page provides two key examples:
- Calculating side length with cosine rule example: Find the length of side BC in a triangle where two sides are 7cm and 3cm, with an included angle of 35°. Example: Using the Cosine Rule: a² = 7² + 3² - 2cos a² = 49 + 9 - 34.40 a² = 23.60 a = √23.60 ≈ 4.9cm
- Finding angle using Cosine Rule calculator: Find the size of angle B in a triangle with sides 4cm, 5cm, and 7cm. Example: Applying the Cosine Rule for angles: cos B = / cos B = / 40 cos B = -0.2 B = cos⁻¹ ≈ 101.5°
These examples illustrate how the Cosine Rule can be used to find both sides and angles in triangles, making it a versatile tool in trigonometry. The page emphasizes the importance of choosing the correct formula based on the given information and what needs to be calculated.
Highlight: When using the Cosine Rule, pay attention to whether you're solving for a side or an angle, as the formulas differ slightly.
Understanding when and how to apply the Cosine Rule is crucial for students tackling complex triangle problems in trigonometry and geometry.
Using Sine and Cosine Rules to Find a Side or Angle in a Triangle
This page provides a decision-making guide for choosing between the Sine Rule and Cosine Rule when solving triangle problems. It helps students understand when to use sine and cosine rule based on the given information.
Highlight: The choice between Sine and Cosine Rules depends on what information is given and what needs to be found.
When finding a side:
- Use the Cosine Rule if you know two sides and the included angle.
- Use the Sine Rule if you know two angles and one side.
When finding an angle:
- Use the Cosine Rule if you know all three sides.
- Use the Sine Rule if you know two sides and an angle .
Definition: The Sine Rule is expressed as a/sin A = b/sin B = c/sin C, where lowercase letters represent sides and uppercase letters represent angles.
Definition: The Cosine Rule for finding a side is a² = b² + c² - 2bc cos A, and for finding an angle is cos A = / .
These formulas provide the foundation for solving various triangle problems, making them essential tools in trigonometry.
We thought you’d never ask...
What is the Knowunity AI companion?
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.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
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