Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
vx =
$m\angle v =$
$m\angle x =$

Explanation:

Step1: Calculate hypotenuse VX

Use Pythagorean theorem:
$$VX = \sqrt{(WV)^2 + (WX)^2} = \sqrt{7^2 + (7\sqrt{3})^2}$$
$$=\sqrt{49 + 147} = \sqrt{196} = 14$$

Step2: Find $m\angle V$

Use tangent ratio:
$$\tan(V) = \frac{WX}{WV} = \frac{7\sqrt{3}}{7} = \sqrt{3}$$
$$m\angle V = \arctan(\sqrt{3}) = 60^\circ$$

Step3: Find $m\angle X$

Use angle sum of triangle:
$$m\angle X = 180^\circ - 90^\circ - 60^\circ = 30^\circ$$

Answer:

$VX = 14$
$m\angle V = 60^\circ$
$m\angle X = 30^\circ$