Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
xz =
$m\angle z =$ $^\circ$
$m\angle x =$ $^\circ$

Explanation:

Step1: Find hypotenuse $XZ$ via Pythagoras

$$XZ = \sqrt{(\sqrt{15})^2 + (3\sqrt{5})^2}$$
$$=\sqrt{15 + 45} = \sqrt{60} = 2\sqrt{15}$$

Step2: Calculate $m\angle Z$ using $\tan$

$$\tan(Z) = \frac{\sqrt{15}}{3\sqrt{5}} = \frac{\sqrt{3}}{3}$$
$$m\angle Z = 30^\circ$$

Step3: Calculate $m\angle X$ (right triangle angle sum)

$$m\angle X = 90^\circ - 30^\circ = 60^\circ$$

Answer:

$XZ = 2\sqrt{15}$
$m\angle Z = 30$
$m\angle X = 60$