Question

In triangle abc angle abc is equal to 90 degree also angle A is half of angle C prove that AC=2BC

Answer 1

Answer:

Step-by-step explanation:

 ∠B = 90°

we know, sum of all angles in a triangle is 180

Hence,

∠A + ∠B + ∠C = 180°

∠C/2 + ∠C = 180° - 90°

3∠C/2 = 90°

∠C = 90° x 2 / 3 = 60°

now, side in a triangle is ∝ to angle opposite to it

AC ∝ ∠B

BC ∝ ∠A

Thus,

AC/BC = B/C

AC/BC = 90°/60° = 3/2

2AC = 3BC