Question

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

Answer 1

ANSWER

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

EXPLANATION

$\sin(x) = \frac{Opposite}{hypotenuse}$

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

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

We use Pythagoras Theorem to find

${ |ZX| }^{2} + {3}^{2} = {4}^{2}$

${ |ZX| }^{2} +9=16$

${ |ZX| }^{2} =16 - 9$

${ |ZX| }^{2} = 7$

${ |ZX| } = \sqrt{7}$

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

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

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

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