Edexcel IGCSE 4MA1 Sine and Cosine Rules: Exam Questions

Edexcel IGCSE 4MA1 Sine and Cosine Rules: Exam Questions and Answers

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

4 worked examples

Higher tier · calculator allowed

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Start with one question on the sine rule. Stuck? Take a hint. No sign-in needed.

In triangle

A B C

a = 10

cm,

A = 40^{\circ}

and

B = 65^{\circ}

. Find

b

Choose your answer · keys 1–4

5.83 cm

16.3 cm

7.09 cm

14.1 cm

What this topic covers

Harder Trigonometry Problems 1: Multi-step trig problems (angles of elevation, bearings).
Area of a Triangle (½ ab sin C): Area = ½ ab sin C for non-right-angled triangles.
Harder Trigonometry in 3D 1: Trig in 3D — angle between line and plane.
Harder Trigonometry in 3D 2: Trig in 3D — angle between two planes.

Sine and Cosine Rules worked examples

Worked example 1: Sine rule

In triangle ABC, angle A = $40^{\circ}$ , angle B = $75^{\circ}$ and BC = 8 cm. Find AC.

Triangle ABC with angle A = 40 degrees, angle B = 75 degrees and BC = 8 cm

Solution

BC is opposite A and AC is opposite B.
$\frac{A C}{\sin 75^{\circ}} = \frac{8}{\sin 40^{\circ}}$ .
$A C = 12.0$ cm (3 s.f.).

4 steps

Tip: Pair each side with its opposite angle.

Worked example 2: Area using ½ab sin C

Find the area of a triangle with sides 7 cm and 10 cm and included angle $30^{\circ}$ .

Triangle with sides 7 cm and 10 cm and an included angle of 30 degrees

Solution

$A = \frac{1}{2} \times 7 \times 10 \times \sin 30^{\circ}$ .
$= 17.5$ cm².

3 steps

Tip: C must be the angle between the two sides.

Worked example 3: Angle between a line and a plane

A cuboid is 5 cm by 5 cm by 8 cm tall. Find the angle between a space diagonal and the base.

Cuboid 5 cm by 5 cm by 8 cm tall; the angle theta between a space diagonal and the base diagonal below it

Solution

Base diagonal: $\sqrt{25 + 25} = \sqrt{50}$ .
$\tan θ = \frac{8}{\sqrt{50}}$ .
$θ = {48.5}^{\circ}$ .

4 steps · 1 to fill in

Tip: The angle is between the line and its projection on the plane.

Worked example 4: Angle between a face and the base

A pyramid has a square base of side 6 cm and vertical height 4 cm. Find the angle between a sloping face and the base.

Square-based pyramid, base 6 cm and vertical height 4 cm; theta is the angle between a sloping face and the base

Solution

From the centre of the base to the midpoint of an edge is 3 cm.
$\tan θ = \frac{4}{3}$ .
$θ = {53.1}^{\circ}$ .

4 steps · 1 to fill in

Tip: Use the midpoint of the base edge, not a corner.

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 sine and cosine rules?

Either Higher tier paper, 1H or 2H, can test sine and cosine rules: 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 sine and cosine rules 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 Sine and Cosine Rules: Exam Questions and Answers

Try it first

What this topic covers

Sine and Cosine Rules worked examples

Worked example 1: Sine rule

Solution

Worked example 2: Area using ½ab sin C

Solution

Worked example 3: Angle between a line and a plane

Solution

Worked example 4: Angle between a face and the base

Solution

Revise sine and cosine rules for the exam

Questions students ask

Practise sine and cosine rules with your progress saved

More Unit 5 topics: Geometry