Question

ve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
$tu = $
$st = $
$m\angle u = \quad ^\circ$
submit

Explanation:

Step1: Calculate side $TU$ (opposite $\angle S$)

Use sine ratio: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(24^\circ)=\frac{TU}{10}$
$TU = 10\times\sin(24^\circ) \approx 10\times0.4067 = 4.1$

Step2: Calculate side $ST$ (adjacent to $\angle S$)

Use cosine ratio: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(24^\circ)=\frac{ST}{10}$
$ST = 10\times\cos(24^\circ) \approx 10\times0.9135 = 9.1$

Step3: Calculate $m\angle U$

Right triangle angles sum to $90^\circ$
$m\angle U = 90^\circ - 24^\circ = 66^\circ$

Answer:

$TU = 4.1$
$ST = 9.1$
$m\angle U = 66^\circ$