Question

In ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC = 7 units. Find ∠B, AB and AC.

Answer 1

Sum of angles in Δle = 180°

∠A + ∠B + ∠C = 180°

45° + ∠B + 90° = 180°

∠B = 180° − 135°

∠B = 45°

From figure `cos B = (BC)/(AB)`

`cos 45^2 =  7/(AB)`

`1/sqrt2 .  7/(AB)`

`AB = 7sqrt2 units`

From figure `sin B = (AC)/(AB)`

`sin 45^@ = (AB)/(7sqrt2)`

`1/sqrt2 = (AC)/(7sqrt2)`

∴ AC =  7 units