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Maths
8 Dec 2025
519
8 pages
Simran @simran_task
A comprehensive guide to GCSE trigonometry practice questions with detailed solutions using SOHCAHTOA principles.
This page introduces fundamental Step-by-step trigonometry solutions GCSE with two starter problems focusing on sine and tangent ratios.
Example Question 1 demonstrates finding a hypotenuse using sine ratio with Sin 35° = 20/x, resulting in x = 34.9
Vocabulary Opposite - The side opposite to the angle in question Adjacent - The side adjacent to the angle in question Hypotenuse - The longest side of a right-angled triangle
This section progresses to more complex calculations involving inverse trigonometric functions.
Example Question 3 uses inverse cosine (cos⁻¹) to find an angle where cos θ = 16/24
Highlight Both questions on this page require understanding of inverse trigonometric functions to find angles rather than sides.
This page focuses on calculating unknown side lengths using trigonometric ratios.
Definition Tangent ratio is used when working with opposite and adjacent sides (TOA in SOHCAHTOA)
Example Question 5 uses tan 35° to find a length of 14.0 units
These questions focus on determining unknown angles using inverse trigonometric functions.
Highlight Question 7 demonstrates the use of inverse sine (sin⁻¹) to find an angle of 18.2°
Example Question 8 uses inverse tangent to calculate an angle of 60.9°
This page introduces more sophisticated problems involving multiple steps.
Example Question 9 requires finding an angle in a complex shape involving multiple right triangles
Highlight The solution requires breaking down the problem into manageable steps using basic trigonometric ratios
This section presents more challenging problems requiring multiple steps and precise calculations.
Example Question 10 involves using the Pythagorean theorem alongside trigonometric ratios
Highlight Solutions must be given to 1 decimal place, emphasizing the importance of accuracy
The worksheet concludes with the most challenging question requiring multiple steps and careful analysis.
Example Question 11 involves finding an angle in a complex triangle setup using multiple trigonometric calculations
Highlight The final answer must be given to 1 decimal place (41.8°)
This page outlines the essential guidelines for approaching these SOHCAHTOA exam problems worksheet. The document is designed for GCSE (1-9) mathematics students.
Highlight Students must use black ink or ball-point pen and show all working out.
Definition SOHCAHTOA is a mnemonic device used to remember the relationships between angles and sides in right-angled triangles.
The page emphasizes proper exam technique including time management and thorough checking of answers.
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
Real questions on past papers. You’re going to do amazing! I believe in you!
MathsExplore the key concepts of central tendency with this summary on median, mean, mode, and range. Learn how to calculate each type of average and understand their significance in statistics. Ideal for students seeking clarity on statistical measures.
ChemistryWhat each rule means.
MathsExplore the essential rules of indices, including division, multiplication, negative and fractional powers. This summary covers key concepts such as evaluating exponents and applying laws of indices to solve complex problems effectively.
MathsExplore the essential laws of indices with detailed explanations of all 7 rules crucial for Year 9 Maths. This summary covers exponent properties, including multiplication, division, and negative indices, providing clear examples to enhance your understanding. Ideal for students seeking to strengthen their grasp of exponent rules.
Maths5 laws of indices!
MathsQuotes from every main character
English LiteratureApp 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
Simran
@simran_task
A comprehensive guide to GCSE trigonometry practice questions with detailed solutions using SOHCAHTOA principles.
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 fundamental Step-by-step trigonometry solutions GCSE with two starter problems focusing on sine and tangent ratios.
Example: Question 1 demonstrates finding a hypotenuse using sine ratio with Sin 35° = 20/x, resulting in x = 34.9
Vocabulary: Opposite - The side opposite to the angle in question Adjacent - The side adjacent to the angle in question Hypotenuse - The longest side of a right-angled triangle
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section progresses to more complex calculations involving inverse trigonometric functions.
Example: Question 3 uses inverse cosine (cos⁻¹) to find an angle where cos θ = 16/24
Highlight: Both questions on this page require understanding of inverse trigonometric functions to find angles rather than sides.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on calculating unknown side lengths using trigonometric ratios.
Definition: Tangent ratio is used when working with opposite and adjacent sides (TOA in SOHCAHTOA)
Example: Question 5 uses tan 35° to find a length of 14.0 units
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
These questions focus on determining unknown angles using inverse trigonometric functions.
Highlight: Question 7 demonstrates the use of inverse sine (sin⁻¹) to find an angle of 18.2°
Example: Question 8 uses inverse tangent to calculate an angle of 60.9°
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 more sophisticated problems involving multiple steps.
Example: Question 9 requires finding an angle in a complex shape involving multiple right triangles
Highlight: The solution requires breaking down the problem into manageable steps using 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 section presents more challenging problems requiring multiple steps and precise calculations.
Example: Question 10 involves using the Pythagorean theorem alongside trigonometric ratios
Highlight: Solutions must be given to 1 decimal place, emphasizing the importance of accuracy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The worksheet concludes with the most challenging question requiring multiple steps and careful analysis.
Example: Question 11 involves finding an angle in a complex triangle setup using multiple trigonometric calculations
Highlight: The final answer must be given to 1 decimal place (41.8°)
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page outlines the essential guidelines for approaching these SOHCAHTOA exam problems worksheet. The document is designed for GCSE (1-9) mathematics students.
Highlight: Students must use black ink or ball-point pen and show all working out.
Definition: SOHCAHTOA is a mnemonic device used to remember the relationships between angles and sides in right-angled triangles.
The page emphasizes proper exam technique including time management and thorough checking of answers.
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
Real questions on past papers. You’re going to do amazing! I believe in you!
MathsExplore the key concepts of central tendency with this summary on median, mean, mode, and range. Learn how to calculate each type of average and understand their significance in statistics. Ideal for students seeking clarity on statistical measures.
ChemistryWhat each rule means.
MathsExplore the essential rules of indices, including division, multiplication, negative and fractional powers. This summary covers key concepts such as evaluating exponents and applying laws of indices to solve complex problems effectively.
MathsExplore the essential laws of indices with detailed explanations of all 7 rules crucial for Year 9 Maths. This summary covers exponent properties, including multiplication, division, and negative indices, providing clear examples to enhance your understanding. Ideal for students seeking to strengthen their grasp of exponent rules.
Maths5 laws of indices!
MathsQuotes from every main character
English LiteratureApp 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
Sociology