Question

In ΔABC, ∠B = 90° , AB = y units, BC = `(sqrt3)` units, AC = 2 units and angle A = x°, find:

1. sin x°
2. x°
3. tan x° 
4. use cos x° to find the value of y.

Answer 1

(i) From Δ ABC,

sin x° = `"perpendicular"/"Hypotenus" = (sqrt3)/(2)`

(ii) sin x° = `(sqrt3)/(2)`

sin x° = sin 60°

x° = 60°

(iii) tan x° = tan 60°

tan x° = `(sqrt3)`

(iv) cos x° = `"y"/2`

cos 60° = `"y"/2`

`1/2 = "y"/2`

`2/2` = y

∴ y = 1