CAIE IGCSE Mathematics 2D Pythagoras and trigonometry

Practise linking Pythagoras’ theorem and trigonometry in two-dimensional diagrams to find lengths, angles and distances in degrees.

Exam points

use a shared side in two right-angled triangles before calculating x or a length
combine Pythagoras with sin, cos or tan to find a distance or angle in a 2D diagram
choose the correct angle in degrees when a bearing or elevation context is implied

[Maximum number: 3]

The diagram shows a circle, centre O, radius 11 cm. C, F, G and H are points on the circumference of the circle.
The line AD touches the circle at C and is parallel to the line EG. B is a point on AD and angle $A B O=140^{\circ}$ .

Calculate BH.

BH= ___ cm

6.11 or 6.112 to 6.114
M1 for $OB^{2}=13.11^{2}+11^{2}$ .
A1 for 17.1 or 17.11 or 17.112 to 17.114.
OR
M1 for $\frac{11}{\sin40}$ oe.
A1 for 17.1 or 17.11... or 17.112 to 17.113.

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C6.2.2 Solve problems in two dimensions using Pythagoras’ theorem and question 1