Trigonometry 2 (AQA GCSE Maths): Revision Notes

Trigonometry 2

Finding missing sides in right-angled triangles

You can use trigonometric ratios to find the length of any missing side in a right-angled triangle when you know the length of one other side and one of the acute angles.

Using SOH CAH TOA

When working with trigonometry, you need to identify which sides of the triangle you're working with relative to the given angle:

• Opposite (opp) - the side directly across from the angle
• Adjacent (adj) - the side next to the angle (but not the hypotenuse)
• Hypotenuse (hyp) - the longest side, always opposite the right angle

The key trigonometric ratios are remembered using SOH CAH TOA:

• Sin = Opposite / Hypotenuse: $\sin = \frac{\text{opp}}{\text{hyp}}$
• Cos = Adjacent / Hypotenuse: $\cos = \frac{\text{adj}}{\text{hyp}}$
• Tan = Opposite / Adjacent: $\tan = \frac{\text{opp}}{\text{adj}}$

Worked example

Here's how to solve for a missing side using the sine ratio:

Angles of elevation and depression

Angles of elevation and angles of depression appear in many trigonometry exam questions, especially those involving real-world scenarios.

Key definitions

• Angle of elevation - the angle measured upwards from the horizontal to an object above eye level
• Angle of depression - the angle measured downwards from the horizontal to an object below eye level

Practice problems

You'll often encounter triangles in different orientations. Here are three common types you should be able to solve:

Key points for practice problems:

• Always start by labelling the sides relative to the angle you're working with
• In problem (c), note that 'a' represents the hypotenuse - be careful when setting up your equation
• Remember to substitute carefully and check your final answer is sensible

Exam tip: Give your answers to 1 decimal place as requested, and always show your working clearly for full marks.