Question

In triangle xyz angle y is a right angle sinx=4/5 then cos z?

Answer 1

Y=90°,
x=37°,
z=53°.

cos z =cos 53°=3/5

Answer 2

The answer is given below :

y = 90°

and

$sinx = \frac{4}{5} \\ \\ or \: \: x = {sin}^{ - 1} ( \frac{4}{5} )$

Now,

$z = 180 - ( {sin}^{ - 1} \frac{4}{5} + 90) \\ \\ = 90- {sin}^{ - 1} \frac{4}{5}$

So,

$cosz = cos(90 - {sin}^{ - 1} \frac{4}{5} ) \\ \\ = sin( {sin}^{ - 1} \frac{4}{5} ) \\ \\ = \frac{4}{5}$

Thank you for your question.