Question

abc is a right triangle and right angled at b such that angle bca=2 angle bac.show that hypotenuse ac=2bc

Answer 1

in triangle ABC B = 90
C = 2 * A
let A = x
then C = 2x
now, sum of angles in a triangle is 180
therefore, x + 2x + 90 = 180
3x = 90
x = 30
therefore,A = 30
C = 2 * A = 60
now sin A = BC / AC
sin 30 = BC / AC
1/2 = BC / AC
AC = 2 * BC
hence proved

Answer 2

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