Right-angled trigonometry
In a right-angled triangle, SOH CAH TOA links an angle to two of the sides. Label the sides from the angle: Opposite, Adjacent (next to it) and Hypotenuse (the longest, opposite the right angle).
Key facts
- sin θ = O/H, cos θ = A/H, tan θ = O/A.
- Label the sides before you choose the rule.
- To find an angle, use the inverse: sin⁻¹, cos⁻¹ or tan⁻¹.
- Make sure your calculator is in degrees.
Worked examples
Example 1
Find x. Give your answer to 1 decimal place.
- From the 35° angle: x is Opposite, 10 cm is the Hypotenuse. O and H: use sin. sin 35 = x/10
- Multiply both sides by 10. x = 10 × sin 35
- Work it out. x = 5.7 cm
Answer: x = 5.7 cm
Example 2
A ramp rises 2 m over a horizontal distance of 5 m. What angle does it make with the ground?
- Opposite 2, Adjacent 5: use tan. tan θ = 2/5
- Inverse tan. θ = tan⁻¹(0.4)
- So θ ≈ 21.8°
Answer: 21.8°