Question

In ΔABC, ∠B = 90°, find ∠A if AB is `sqrt(3)` times BC.

Answer 1

Given: In ΔABC, ∠B = 90° and AB = `sqrt(3)`·BC.

Step-wise calculation:

1. Let BC = x, so AB = `sqrt(3)x`. 

2. For angle A, the side opposite is BC (x) and the side adjacent is AB (`sqrt(3)x`). 

3. Therefore, `tan A = "Opposite"/"Adjacent"` 

= `x/(sqrt(3) x)`

= `1/sqrt(3)` 

4. Since `tan 30^circ = 1/sqrt(3)`, ∠A = 30°.