20.3 Angles of elevation and depression — 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.
- Work out on your calculator in degree mode.
- In a right-angled triangle, name the side next to an angle, other than the hypotenuse.
Answers
- . 2. The adjacent side.
If an answer differs, revisit Section 20.2 for the sine ratio and for naming the sides of a right-angled triangle.
Practise with help
1. A 10 m ramp rises at 30°. Find its vertical rise.
Hint
The ramp is the hypotenuse; rise is opposite.
Full working
sin 30° = h/10, so h = 5 m.
2. A 12 m flagpole is viewed at 45°. Find horizontal distance.
Hint
Height is opposite and distance is adjacent.
Full working
tan 45° = 12/d, so d = 12 m.
3. A 20 m tower is viewed from 25 m away. Find elevation angle.
Hint
Use tangent with opposite and adjacent.
Full working
tan θ = 20/25, so θ ≈ 38.7°.
Before opening each full working, name the method and explain which measurements led you to choose it.