Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
yz =
xz =
m∠y = °

Explanation:

Step1: Find $\angle Y$

Sum of triangle angles is $180^\circ$.
$m\angle Y = 180^\circ - 90^\circ - 60^\circ = 30^\circ$

Step2: Calculate $XZ$

Use $\tan(60^\circ)=\frac{XY}{XZ}$
$\tan(60^\circ)=\sqrt{3}$, so $XZ = \frac{XY}{\tan(60^\circ)} = \frac{6\sqrt{3}}{\sqrt{3}} = 6$

Step3: Calculate $YZ$

Use $\cos(60^\circ)=\frac{XZ}{YZ}$
$\cos(60^\circ)=\frac{1}{2}$, so $YZ = \frac{XZ}{\cos(60^\circ)} = \frac{6}{\frac{1}{2}} = 12$

Answer:

$YZ = 12$
$XZ = 6$
$m\angle Y = 30^\circ$