Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round
$m\angle u =$
$tv =$
$tu =$

Explanation:

Step1: Find $m\angle U$

In a right - triangle, the sum of angles is $180^{\circ}$. Since it's a right - triangle ($\angle V = 90^{\circ}$) and $\angle T=30^{\circ}$, then $m\angle U=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ}$.

Step2: Find $TU$ (hypotenuse)

In a $30 - 60 - 90$ right - triangle, if the side opposite the $30^{\circ}$ angle ($VU$) is $a = 5$, then the hypotenuse $TU = 2a$. So $TU = 2\times5=10$.

Step3: Find $TV$

In a $30 - 60 - 90$ right - triangle, if the side opposite the $30^{\circ}$ angle ($VU$) is $a = 5$, then the side opposite the $60^{\circ}$ angle ($TV$) is $a\sqrt{3}$. So $TV = 5\sqrt{3}$.

Answer:

$m\angle U = 60^{\circ}$, $TV = 5\sqrt{3}$, $TU = 10$