To find a side, write the ratio and rearrange. If tan 44° = DF/9.5, then DF = 9.5 × tan 44° = 9.17 cm. If the unknown is on the bottom of the fraction, divide instead: hypotenuse = opposite ÷ sin θ.
To find an angle, use the inverse functions sin⁻¹, cos⁻¹ and tan⁻¹ on a calculator. If cos θ = 5/12.4, then θ = cos⁻¹(5/12.4) = 66.2°. Make sure your calculator is in degrees, and round only at the end.
Worked example
In triangle PQR, ∠Q = 90°, PR = 14 cm and ∠P = 38°. Find QR to 3 s.f.
- QR is opposite P and PR is the hypotenuse, so use sine.
- QR = 14 × sin 38° = 8.619…
Answer:8.62 cm
Key words
- inverse sine (sin⁻¹)
- finds an angle from a ratio
- degrees mode
- the calculator setting for angles in °
- significant figures
- a way of rounding
Practise this
New questions every time.
Common Core-referenced: HSG-SRT.C.8