How it works

In a right-angled triangle, SOHCAHTOA reminds us that sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent. Choose the ratio based on which two sides (or angle and side) are known or required, then rearrange to solve for the missing value using a calculator in degree mode.

The method

1. 1.Label the sides as opposite, adjacent and hypotenuse relative to the known angle
2. 2.Choose sin, cos or tan based on which two sides are involved
3. 3.Set up the equation and rearrange to solve for the unknown
4. 4.Use inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to find an angle

Worked example

Find x in a right triangle with hypotenuse 10cm and angle 30° opposite side x.

1. sin(30°) = x/10
2. x = 10 × sin(30°) = 5cm

Worked example

Find angle θ where opposite = 7cm and adjacent = 9cm.

1. tan(θ) = 7/9
2. θ = tan⁻¹(7/9) = 37.9° (1 d.p.)

Common mistakes

• Labelling the opposite and adjacent sides incorrectly relative to the angle
• Using the wrong trig ratio for the given information
• Calculator set to radians instead of degrees