Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
vw =
uv =
m∠w = °

Explanation:

Step1: Find $\angle W$

The sum of angles in a triangle is $180^\circ$.
$m\angle W = 180^\circ - 90^\circ - 60^\circ = 30^\circ$

Step2: Calculate $UV$ (adjacent to $\angle U$)

Use cosine of $\angle U$: $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos60^\circ=\frac{UV}{6} \implies UV = 6\times\cos60^\circ = 6\times\frac{1}{2}=3$

Step3: Calculate $VW$ (opposite to $\angle U$)

Use sine of $\angle U$: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin60^\circ=\frac{VW}{6} \implies VW = 6\times\frac{\sqrt{3}}{2}=3\sqrt{3}$

Answer:

$VW = 3\sqrt{3}$
$UV = 3$
$m\angle W = 30^\circ$