20.2 Trigonometric ratios (SOHCAHTOA) — Practise with help
Try each problem first. Open a hint if you need it, then use the working to check your method.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Simplify .
- In a right-angled triangle, which side is opposite the right angle?
Answers
- . 2. The hypotenuse.
If an answer differs, revisit Section 4.1 for simplifying fractions and Section 20.1 for naming the sides of a right-angled triangle.
Practise with help
1. Find the opposite side for hypotenuse 12 and angle 30°.
Hint
Use sine: opposite over hypotenuse.
Full working
sin 30° = x/12, so x = 6.
2. Find the adjacent side for hypotenuse 10 and angle 60°.
Hint
Use cosine.
Full working
cos 60° = x/10, so x = 5.
3. Opposite is 8 and adjacent is 15. Find the angle.
Hint
Use tangent, then inverse tangent.
Full working
tan θ = 8/15, so θ ≈ 28.1°.
Before opening each full working, name the method and explain which measurements led you to choose it.