Question

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

Answer 1

`\tan(x) = (3√(7))/(7)`

Step-by-step explanation

`\sin(x) = (Opposite)/(hypotenuse)`

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

This means the opposite side is 3 units and the hypotenuse is 4 units.

We use Pythagoras Theorem to find

`^(2) + {3}^(2) = {4}^(2)`

`^(2) +9=16`

`^(2) =16 - 9`

`^(2) = 7`

`= √(7)`

`\tan(x) = (opposite)/(adjacent)`

`\tan(x) = (3)/( √(7) )`

`\tan(x) = (3)/( √(7) ) * (√(7))/(√(7))`

`\tan(x) = (3√(7))/(7)`