Question

in $\triangle uvw$, the measure of $\angle w = 90^\circ$, $uw = 36$, $wv = 77$, and $vu = 85$. what ratio represents the sine of $\angle u$?

Explanation:

Step1: Recall sine definition for right triangles

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle U$

• Opposite side to $\angle U$: $WV = 77$
• Hypotenuse (longest side): $VU = 85$

Step3: Substitute values into sine ratio

$\sin(\angle U) = \frac{\text{Length of } WV}{\text{Length of } VU}$

Answer:

$\frac{77}{85}$