Question

in the given fig abc is a right triangle and right angled at B such that angle Bca=2angle BAc show that hypotenuse Ac =2bc​

Answer 1

hey

here

GIVEN➡BCA=2BAC---------------1.)

In ∆ABC

➡angle BCA+ angle CBA + angle BAC = 180°

➡2 angle BAC + 90 + angle BAC = 180° [ from-1 ]

➡3 angle BAC = 90°

➡angle BAC = 90/3

➡angle BAC=30° and BCA=2×30=60°

Better use trigonometry

➡sin30=BC/AC

➡1/2=BC/AC

➡AC=2BC

(proved)