Question

In ΔABC, ∠B = 90°. If `(AB)/(AC) = 1/2`, then cos C is equal to ______.

Options

• `3/2`

• `1/2`

• `sqrt(3)/2`

• `1/sqrt(3)`

Answer 1

In ΔABC, ∠B = 90°. If `(AB)/(AC) = 1/2`, then cos C is equal to `underlinebb(sqrt(3)/2)`.

Explanation:

Given `(AB)/(AC) = 1/2`

Let AB = K, AC = 2K

By Pythagoras theorem,

AC² = AB² + BC²

(2K)² – K² = BC²

3K² = BC²

BC = `sqrt(3)"K"`

cos C = `(BC)/(AC)`

cos C = `(sqrt(3)K)/(2K)`

cos C = `sqrt(3)/2`