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## 15 Trigonometry Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

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Trigonometry questions address the relationship between the angles of a triangle and the lengths of its sides. By using our knowledge of the rules of trigonometry we can calculate missing angles or sides when we have been given some of the information.

Here we’ve provided 15 trigonometry questions to provide students with practice at the various sorts of trigonometry problems and GCSE exam style questions you can expect in KS3 and KS4 trigonometry.

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Free GCSE maths revision resources for schools As part of the Third Space Learning offer to schools, the personalised online GCSE maths tuition can be supplemented by hundreds of free GCSE maths revision resources including: – GCSE maths past papers – GCSE maths worksheets – GCSE maths questions – GCSE maths topic list

## Trigonometry in the real world

Trigonometry is used by architects, engineers, astronomers, crime scene investigators, flight engineers and many others.

## Trigonometry in KS3 and KS4

In KS3 we learn about the trigonometric ratios sin, cos and tan and how we can use these to calculate sides and angles in right angled triangles. In KS4 trigonometry involves applying this to a variety of situations as well as learning the exact values of sin, cos and tan for certain angles.

In the higher GCSE syllabus we learn about the sine rule, the cosine rule, a new formula for the area of a triangle and we apply trigonometry to 3D shapes. In A Level maths trigonometry is developed further but that is not the focus of the trigonometry questions here.

## Download this 15 Trigonometry Questions And Practice Problems (KS3 & KS4) Worksheet

Help your students prepare for their Maths GSCE with this free Trigonometry worksheet of 15 multiple choice questions and answers.

## How to answer trigonometry questions

The way to answer trigonometry questions depends on whether it is a right angled triangle or not.

## How to answer trigonometry questions: right-angled triangles

If your trigonometry question involves a right angled triangle, you can apply the following relationships ie SOH, CAH, TOA

To answer the trigonometry question:

1 . Establish that it is a right angled triangle.

2 . Label the opposite side (opposite the angle) the adjacent side (next to the angle) and the hypotenuse (longest side opposite the right angle).

3. Use the following triangles to help us decide which calculation to do:

## How to answer trigonometry questions – non-right angled triangles

If the triangle is not a right angled triangle then we need to use the sine rule or the cosine rule.

There is also a formula we can use for the area of a triangle, which does not require us to know the base and height of the triangle.

- Establish that it is not a right angled triangle.
- Label the sides of the triangle using lower case a, b, c.
- Label the angles of the triangle using upper case A, B and C.
- Opposite sides and angles should use the same letter so for example angle C is opposite to side c.

## KS3 trigonometry questions

In KS3 trigonometry questions focus on understanding of sin, cos and tan (SOHCAHTOA) to calculate missing sides and angles in right triangles.

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## KS3 trigonometry questions – missing side

1. A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10^{\circ} to the horizontal. Calculate the length of the zip wire.

2. A surveyor wants to know the height of a skyscraper. He places his inclinometer on a tripod 1m from the ground. At a distance of 50m from the skyscraper, he records an angle of elevation of 82^{\circ} .

What is the height of the skyscraper? Give your answer to one decimal place.

Total height = 355.8+1=356.8m.

3. Triangle ABC is isosceles. Work out the height of triangle ABC.

To solve this we split the triangle into two right angled triangles.

4. A builder is constructing a roof. The wood he is using for the sloped section of the roof is 4m long and the peak of the roof needs to be 2m high. What angle should the piece of wood make with the base of the roof?

5. A ladder is leaning against a wall. The ladder is 1.8m long and the bottom of the ladder is 0.5m from the base of the wall. To be considered safe, a ladder must form an angle of between 70^{\circ} and 80^{\circ} with the floor. Is this ladder safe?

Not enough information

Yes it is safe.

6. A helicopter flies 40km east followed by 105km south. On what bearing must the helicopter fly to return home directly?

Since bearings are measured clockwise from North, we need to do 360-21=339^{\circ}.

## KS4 trigonometry questions

In KS4 maths, trigonometry questions ask students to solve a variety of problems including multi step problems and real life problems. We also need to be familiar with the exact values of the trigonometric functions at certain angles.

In the higher syllabus we look at applying trigonometry to 3D problems as well as using the sine rule, cosine rule and area of a triangle.

Trigonometry is covered by all exam boards, including Edexcel, AQA and OCR.

Read more: Question Level Analysis Of Edexcel Maths Past Papers (Foundation)

7. Calculate the size of angle ABC. Give your answer to 3 significant figures.

8. Kevin’s garden is in the shape of an isosceles trapezium (the sloping sides are equal in length). Kevin wants to buy enough grass seed for his garden. Each box of grass seed covers 15m^2 . How many boxes of grass seed will Kevin need to buy?

To calculate the area of the trapezium, we first need to find the height. Since it is an isosceles trapezium, it is symmetrical and we can create a right angled triangle with a base of \frac{10-5}{2} .

We can then find the area of the trapezium:

Number of boxes: 88.215=5.88

Kevin will need 6 boxes.

9. Which of these values cannot be the value of \sin(\theta) ?

10. . Write 4sin(60) + 3tan(60) in the form a\sqrt{k}.

Work out angle a, between the line AG and the plane ADHE.

We need to begin by finding the length AH by looking at the triangle AEH and using pythagoras theorem.

\begin{aligned} &AH^2=14^2+3^2 \\\\ &AH^2=205 \\\\ &AH=14.32cm \end{aligned}

We can then find angle a by looking at the triangle AGH.

\begin{aligned} \tan(\theta)&=\frac{O}{A}\\\\ \tan(\theta)&=\frac{4}{14.32}\\\\ \theta&=tan^{-1}(\frac{4}{14.32})\\\\ \theta&=15.6^{\circ} \end{aligned}

12. Work out the length of BC.

First we need to find the length DC by looking at triangle CDE.

We can then look at triangle BAC.

13. Ship A sails 40km due West and ship B sails 65km on a bearing of 050^{\circ} . Find the distance between the two ships.

The angle between their two paths is 90+50=140^{\circ} .

\begin{aligned} a^{2}&=b^{2}+c^{2}-2bc \cos(A)\\\\ a^{2}&=40^{2}+65^{2}-2\times 40 \times 65 \cos(140)\\\\ a^{2}&=5825-5200 \cos(140)\\\\ a^{2}&=9808.43\\\\ a&=99.0\mathrm{km} \end{aligned}

14. Find the size of angle B.

First we need to look at the right angled triangle.

Then we can look at the scalene triangle.

The area of the triangle is 16cm^2 . Find the length of the side x .

\begin{aligned} \text{Area }&=\frac{1}{2}ab \sin(C)\\\\ 16&=\frac{1}{2} \times x \times 2x \times \sin(40)\\\\ 16&=x^{2} \sin(40)\\\\ \frac{1}{\sin(40)}&=x^{2}\\\\ 24.89&=x^{2}\\\\ 5.0&=x \end{aligned}

Third Space Learning’s free GCSE maths resource library contains detailed lessons with step-by-step instructions on how to solve ratio problems, as well as worksheets with trigonometry practice questions and more GCSE exam questions.

Take a look at the trigonometry lessons today – more are added every week.

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Do you have students who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary students become more confident, able mathematicians. Find out more about our GCSE Maths tuition or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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Trigonometry Practice Questions Click here for Questions . Click here for Answers . Answers - Version 1 Answers - Version 2 GCSE Revision Cards 5-a-day Workbooks Primary Study Cards Contact us Privacy Policy Terms and Conditions GDPR The Corbettmaths Practice Questions on Trigonometry

The Corbettmaths Textbook Exercise on Trigonometry. Corbettmaths Videos, worksheets, 5-a-day and much more ... About; Revision Cards; Books; October 7, 2019 October 9, 2023 corbettmaths. Trigonometry Textbook Exercise Click here for Questions. Textbook Exercise; Post navigation.

The Corbettmaths Practice Questions on Exact Trig Values. Videos, worksheets, 5-a-day and much more

5. A ladder is placed against a wall. To be safe, it must be inclined at between 700 and 800 to the ground. Is the ladder safe? Calculate the length of the ladder. ......................... (3) .........................m (3) 6. The diagram shows two right-angled triangles. Calculate the value of x. .........................cm (5) 7.

Trigonometry Equipment needed: Calculator, pen Guidance Read each question carefully before you begin answering it. Check your answers seem right. Always show your workings Video Tutorial www.corbettmaths.com/contents Videos 329, 330, 331 Answers and Video Solutions Shown below is a right-angled triangle.

Practice Questions. Previous FM Trigonometric Identities Questions. Next FM Trigonometric Ratios Questions. The Corbettmaths Practice Questions on Solving Trigonometric Equations for Level 2 Further Maths.

The Corbettmaths Practice Questions on Advanced Trigonometry for Level 2 Further Maths.

These are the Corbettmaths Textbook Exercise answers to Trigonometry

Posts about trigonometry written by corbettmaths. Videos, worksheets, 5-a-day and much more

Question 1: Find the size of the missing angles in the triangles below. Question 2: Find the lengths of the sides labelled x below. 3: Find the size of the missing angles/sides labelled x below. (c) (d) (e) (f) Apply

Question,4:,,,,Find,the,length,of,the,missing,side,in,each,of,these,triangles., , Give,each,answer,to,one,decimal,place. (a), , , , , (b), , , , (c)

L i k e Share 7.6K views 2 months ago Video Tutorials This is part 2 of 3 of a trigonometry review. It covers finding missing sides of right angled triangles if given a side and an angle....

The video solutions to the Corbettmaths Practice Questions on Trigonometry.Practice Questions: https://corbettmaths.com/2019/08/29/trigonometry-practice-ques...

15 Trigonometry c a b A CB 5 cm 9 cm 14 cm 6 cm X Y Z. MEP Y9 Practice Book B 149 Solution In this triangle, YZ 2 =XY XZ22+ 14 2 =XY 2 +6 2 196 =XY 2 +36 XY 2 =160 XY = 160 = 12.64911064 cm =12.6 cm (to 1 decimal place) Example 3 Determine whether or not this triangle contains a right angle. Solution

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Questions on Angles in a Triangle. Corbettmaths Primary Primary 5-a-day, videos, worksheets and more. Menu Skip to content. Home; Videos and Worksheets; 5-a-day; Study Cards; Practice Papers; May 31, 2018 October 12, 2023 corbettmaths. Angles in a Triangle Questions Worksheets;

TRIGONOMETRY Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number.

Learn and revise trigonometric ratios of sine, cosine and tangent and calculate angles and lengths in right-angled triangles with GCSE Bitesize AQA Maths.

The Corbettmaths How Questions on Truing Graphs. Please here for Questions. Click hier for Replies. Trig, Sin, Sine, Cos, Cosine, Tan, Tangent

A set of 10 questions to test your knowledge of trigonometry, the branch of maths that calculates angles and lengths in right-angled triangles. The questions cover the three trigonometric ratios (sine, cosine and tangent) and their applications, such as finding the size of an angle or the length of a side. You can check your score at the end.

GCSE OCR Trigonometry - OCR Angles of elevation and depression The three trigonometric ratios; sine, cosine and tangent are used to calculate angles and lengths in right-angled triangles. The...

To answer the trigonometry question: 1. Establish that it is a right angled triangle. 2. Label the opposite side (opposite the angle) the adjacent side (next to the angle) and the hypotenuse (longest side opposite the right angle). 3. Use the following triangles to help us decide which calculation to do:

The Corbettmaths Practice Questions on Advanced Trigonometry. Corbettmaths Videos, worksheets, 5-a-day and much more. Menu Skip to content. Welcome; Videos and Worksheets; Primary; ... Previous 3D Trigonometry Practice Questions. Next Exact Trigonometric Values Practice Questions. GCSE Revision Cards. 5-a-day Workbooks. Primary Study Cards ...