Question

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

Answer 1

`{ \tan(y) } = ( √(7) )/(3)`

Step-by-step explanation

If

`\sin(X )= (3)/(4)`

`\sin(X )= (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}= √(7)`

`{ \tan(y) } = (opposite)/(adjacent)`

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

`{ \tan(y) } = ( √(7) )/(3)`