IGCSE Math Revision Questions by topic Revision notes Past papers Student hub

Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

IGCSE Maths Sine and Cosine Rules 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.

Practise sine and cosine rules in Unit 5 →Sine and Cosine Rules revision notes

What this topic covers

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.

Solution

  1. BC is opposite A and AC is opposite B.
  2. \(\dfrac{AC}{\sin75^\circ}=\dfrac{8}{\sin40^\circ}\).
  3. \(AC=12.0\) cm (3 s.f.).

Answer: 12.0 cm

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 \(30^\circ\).

Solution

  1. \(A=\tfrac{1}{2}\times7\times10\times\sin30^\circ\).
  2. \(=17.5\) cm².

Answer: 17.5 cm²

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.

Solution

  1. Base diagonal: \(\sqrt{25+25}=\sqrt{50}\).
  2. \(\tan\theta=\dfrac{8}{\sqrt{50}}\).
  3. \(\theta=48.5^\circ\).

Answer: 48.5°

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.

Solution

  1. From the centre of the base to the midpoint of an edge is 3 cm.
  2. \(\tan\theta=\dfrac{4}{3}\).
  3. \(\theta=53.1^\circ\).

Answer: 53.1°

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.

Revise sine and cosine rules for the exam

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.

More Unit 5 topics: Geometry