Question

In a right angled ΔABC, ∠A = 90° and AB = AC. The value of sin C is ______.

Options

• 0

• `sqrt3/2`

• `1/2`

• `1/sqrt2`

Answer 1

In a right angled ΔABC, ∠A = 90° and AB = AC. The value of sin C is `bbunderline(1/sqrt2)`.

Explanation:

Given, a right angled ΔABC, right angled at A and AB = AC

Let AB = AC = a

∵ BC² = AC² + AB²  ...[by Pythagoras theorem]

∴ BC² = a² + a²

∴ BC = `sqrt2  a`

∴ sin C = `(AC)/(BC)`

= `a/(sqrt2  a)`

= `1/sqrt2`

Hence, the value of sin C is `1/sqrt2`.