Question

In triangle XYZ, angle Z is a right angle. If sinX = 3/4, find tan Y.

Answer 1

ANSWER

${ \tan(y) } = \frac{ \sqrt{7} }{3}$

EXPLANATION

If

$\sin(X )= \frac{3}{4}$

$\sin(X )= \frac{opposite}{hypotenuse}$

This implies that the opposite is 3 units and the hypotenuse is 4 units.

We now find the adjacent side using the Pythagoras Theorem.

${a}^{2} + {o}^{2} = {h}^{2}$

${a}^{2} + {3}^{2} = {4}^{2}$

${a}^{2} + 9 =16$

${a}^{2} =16 - 9$

${a}^{2} = 7$

${a}= \sqrt{7}$

${ \tan(y) } = \frac{opposite}{adjacent}$

The side opposite to Y is √7 and the side adjacent to Y is 3.

${ \tan(y) } = \frac{ \sqrt{7} }{3}$