Question

find $uw$.
write your answer as an integer or as a decimal rounded to the nearest tenth.
$uw = \square$

Explanation:

Step1: Identify adjacent side, angle

We know $\angle U = 21^\circ$, adjacent side $UV = 7.8$, $UW$ is the hypotenuse.

Step2: Use cosine ratio formula

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(21^\circ) = \frac{UV}{UW}$
Rearrange to solve for $UW$: $UW = \frac{UV}{\cos(21^\circ)}$

Step3: Substitute values and calculate

$\cos(21^\circ) \approx 0.9336$, so $UW = \frac{7.8}{0.9336} \approx 8.4$

Answer:

8.4