Right-angled trigonometry · Year 10
In Year 10 you learn: finding angles with trigonometry.
Trigonometry links the angles and sides of right-angled triangles. Label the sides from the angle you are using (opposite, adjacent, hypotenuse), choose sin, cos or tan with SOH CAH TOA, and you can find any missing side or angle.
Key facts
- Hypotenuse: the longest side, opposite the right angle. Opposite: across from θ. Adjacent: next to θ.
- SOH: sin θ = opposite ÷ hypotenuse.
- CAH: cos θ = adjacent ÷ hypotenuse.
- TOA: tan θ = opposite ÷ adjacent.
- To find an angle, use the inverse: θ = sin⁻¹(…), cos⁻¹(…) or tan⁻¹(…).
Worked examples
Example 1
Find x, to 1 d.p.
Answer: x = 12.6 cm
Example 2
A ramp rises 1.2 m over a sloping length of 8 m. What angle does it make with the ground, to 1 d.p.?
Answer: 8.6°