Question

If cos A = 8/17, then sin A is
(a) 17/8
(b) 15/17
(c) 17/15 (d) 8/15​

Answer 1

Cos A = 8/17

cos^2 A = 64/289

sin^2A = 225/289

sinA = 15/17

Answer 2

Question :-

If cos A = 8/17, then sin A is

(a) 17/8

(b) 15/17

(c) 17/15 (d) 8/15​

Solution :-

Given ,

Cos A = 8/17

Then sin A = ?

Cos A = adjacent side to Angle A /Hypotenuse.

So , adjacent side is 8 and hypotenuse is 17

For Sin A ,

Sin A = Opposite side/hypotenuse

We need to find opposite side to angle A value.

So , let us consider a right angled triangle named ABC where it is right angled at B .

Using pythagoras theorem,

$AC^{2}=AB^{2}+BC^{2}$

$17^{2} = AB^{2} + 8^{2}$

=> 289 = AB^2 + 64

=> AB^2 = 289-64

=> AB^2 = 225

=> AB = $\sqrt{225}$

=> AB = 15

So ,

Sin A = AB/AC

Sin A = 15/17

Option (b) is right