Core Chapter 7: Right-Angled Triangle Trigonometry

Question 1

Identify the sides of a right-angled triangle

Answer 1

1) Hypotenuse
- Longest side of the triangle (opposite the right-angle)

2) Adjacent
- Side adjacent to θ, containing both θ and the right-angle

3) Opposite
- Side opposite to θ, containing the right-angle

Question 2

State the 3 trigonometric ratios, and use the trigonometric ratios to find:
- An unknown side (given 1 side and θ)
- An unknown angle (given 2 sides)

Answer 2

sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj

And since:
sinθ/cosθ
= opp/hyp / adj/hyp
= opp/adj
= tanθ

sinθ/cosθ = tanθ

Question 3

Define angle of elevation/depression to solve trigonometric problems

Answer 3

Angle of elevation: angle between the horizontal and the line of sight when looking upwards

Angle of depression: angle between the horizontal and line of sight when looking downwards

Question 4

Find true bearings

Answer 4

True bearings: Angles written in 3 digits to describe the direction of one object from another by comparing its angle from True North
- Find bearing of B from A (angle from North to B at A)
Eg. 048° or 138°