Question

In a right angled triangle the hypotenuse is 2√2 times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are

(A) π/2 & π/6

(B) π/8 & 3π/8

(C) π/4 & π/4

(D) π/5 & 3π/10

Answer 1

Correct option (B) π/8 & 3π/8

Explanation:

AC = x/(sin∠ACD) = x/sinC

AB = x/sinB

x²(1/sin²C + 1/sin²B) = 8x²

sin²B + sin²C = 8sin²C sin²B

1 = 8sin²C cos²C

(sin2C) = 1/√2 ⇒ C = π/8 ⇒ B = 3π/8

Comments

Very helpful