Question

In right-angled triangle ABC; ∠B = 90°. Find the magnitude of angle A, if:
a. AB is `sqrt(3)` times of BC.
B. BC is `sqrt(3)` times of BC.

Answer 1

Consider the following figure,

a. Given, AB = `sqrt(3) xx "BC"`

⇒ `"AB"/"BC" = sqrt(3)`
⇒ cot θ = `sqrt(3)`
⇒ cot θ = cot30°
⇒ θ = 30°.
b. Given, BC = `sqrt(3) xx "AB"`

⇒ `"BC"/"AB" = sqrt(3)`
⇒ tan θ = `sqrt(3)`
⇒ tan θ = tan60°
⇒ θ = 60°.