Question

In ΔABC, ∠B = 90° and ∠A is double ∠C. Find `(AB)/(AC)`.

Answer 1

Given:

In triangle ΔABC 

∠B = 90°

∠A = 2 × ∠C

Required `(AB)/(AC)`

Step 1:

let C = x

∠A = 2x

= ∠A + ∠B + ∠C = 180°    ...[using angle sum of triangle]

= 2x + 90° + x = 180°

= 3x = 90° 

= x = 30°

∠C = 30°

∠A = 60°

Step 2:

ΔABC, right-angled at B

sin(∠C), `(AB)/(AC)`

= sin(30°) = `(AB)/(AC)`

= `1/2`