In a right-angled triangle the side opposite $\theta$ is 7 cm and the adjacent side is 10 cm. Find $\theta$.

$\tan\theta=\dfrac{7}{10}$. $\theta=\tan^{-1}0.7=35.0^\circ$. Answer: 35.0°

Edexcel IGCSE 4MA1 Right-Angled Trigonometry: Exam Questions

Edexcel IGCSE 4MA1 Right-Angled Trigonometry: Exam Questions and Answers

Right-Angled Trigonometry questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then cover each solution and redo it yourself.

5 worked examples

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Start with one question on right-angled trigonometry. Stuck? Take a hint. No sign-in needed.

In a right-angled triangle, the side adjacent to a

28^{\circ}

angle is

12

cm. Find the opposite side.

Choose your answer · keys 1–4

6.38 cm

10.6 cm

22.6 cm

5.63 cm

What this topic covers

Pythagoras & right-angle trig (SOH-CAH-TOA): Finding missing sides and angles in right-angled triangles.
Trigonometry 1: SOH CAH TOA — finding an unknown side.
Trigonometry 2: SOH CAH TOA — finding an unknown angle.
Trigonometry 3: Sine rule for non-right-angled triangles.
Trigonometry 4: Cosine rule for non-right-angled triangles.

Right-Angled Trigonometry worked examples

Worked example 1: Finding a side with sine

A right-angled triangle has hypotenuse 10 cm and an angle of 35°. Find the side opposite the 35° angle.

Solution

Opposite and hypotenuse, so use sine: $\sin 35^{\circ} = \frac{x}{10}$ .
$x = 10 \sin 35^{\circ} = 5.735 \dots$
$x = 5.74$ cm (3 s.f.).

4 steps

Tip: Check your calculator is in degrees.

Worked example 2: Finding a side with tan

In a right-angled triangle the side adjacent to a $40^{\circ}$ angle is 14 cm. Find the opposite side.

Right-angled triangle: the side adjacent to the 40 degree angle is 14 cm; the opposite side is x

Solution

$\tan 40^{\circ} = \frac{x}{14}$ .
$x = 14 \tan 40^{\circ} = 11.7$ cm (3 s.f.).

3 steps

Tip: Label O, A, H before choosing the ratio.

Worked example 3: Finding an angle

In a right-angled triangle the side opposite $θ$ is 7 cm and the adjacent side is 10 cm. Find $θ$ .

Right-angled triangle: opposite side 7 cm and adjacent side 10 cm to the angle theta

Solution

$\tan θ = \frac{7}{10}$ .
$θ = \tan^{- 1} 0.7 = {35.0}^{\circ}$ .

3 steps

Tip: Use the inverse function to find an angle.

Worked example 4: Angle of elevation

From 12 m away on level ground, the angle of elevation of the top of a tree is $28^{\circ}$ . Find the height of the tree.

Angle of elevation 28 degrees to the top of a tree 12 m away on level ground; the height h is unknown

Solution

$\tan 28^{\circ} = \frac{h}{12}$ .
$h = 12 \tan 28^{\circ} = 6.38$ m.

3 steps

Tip: Elevation is measured up from the horizontal.

Worked example 5: Choosing the ratio

Triangle ABC has a right angle at C, AB = 9 cm and angle A = $52^{\circ}$ . Find BC.

Triangle ABC with a right angle at C, AB = 9 cm and angle A = 52 degrees

Solution

AB is the hypotenuse and BC is opposite A, so use sine.
$B C = 9 \sin 52^{\circ} = 7.09$ cm.

3 steps

Tip: SOH CAH TOA.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Questions students ask

Which Edexcel IGCSE Maths papers test right-angled trigonometry?

Either Higher tier paper, 1H or 2H, can test right-angled trigonometry: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more right-angled trigonometry questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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Edexcel IGCSE 4MA1 Right-Angled Trigonometry: Exam Questions and Answers

Try it first

What this topic covers

Right-Angled Trigonometry worked examples

Worked example 1: Finding a side with sine

Solution

Worked example 2: Finding a side with tan

Solution

Worked example 3: Finding an angle

Solution

Worked example 4: Angle of elevation

Solution

Worked example 5: Choosing the ratio

Solution

Revise right-angled trigonometry for the exam

Questions students ask

Practise right-angled trigonometry with your progress saved

More Unit 5 topics: Geometry