Question

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

Explanation:

Step1: Identify unknown side $VU$

Use Pythagorean theorem:
$$VU = \sqrt{VT^2 - TU^2} = \sqrt{85^2 - 36^2}$$
Calculate:
$$85^2=7225, 36^2=1296$$
$$VU = \sqrt{7225-1296} = \sqrt{5929} = 77$$

Step2: Define sine of $\angle T$

Sine = opposite/hypotenuse:
$$\sin(T) = \frac{VU}{VT}$$

Step3: Substitute values

$$\sin(T) = \frac{77}{85}$$

Answer:

$\frac{77}{85}$