Question

find the sine of $\angle u$. simplify your answer and write it as a proper fraction, improper fraction, or whole number. $\sin (u) = \square$

Explanation:

Step1: Find side TV via Pythagoras

$$TV = \sqrt{TU^2 - VU^2} = \sqrt{37^2 - 12^2} = \sqrt{1369 - 144} = \sqrt{1225} = 35$$

Step2: Define sine of ∠U

$$\sin(U) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{TV}{TU}$$

Step3: Substitute values

$$\sin(U) = \frac{35}{37}$$

Answer:

$\frac{35}{37}$