Question

find uv.
write your answer as an integer or as a decimal rounded to the nearest tenth.
uv =

Explanation:

Step1: Identify adjacent side, hypotenuse

In right $\triangle UVT$, $\angle U=42^\circ$, hypotenuse $UT=6$, $UV$ is adjacent to $\angle U$.

Step2: Use cosine ratio

Cosine of angle = $\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(42^\circ) = \frac{UV}{6}$

Step3: Solve for UV

Rearrange to isolate $UV$:
$UV = 6 \times \cos(42^\circ)$
Calculate $\cos(42^\circ) \approx 0.7431$, so:
$UV \approx 6 \times 0.7431 = 4.4586$
Round to nearest tenth: $UV \approx 4.5$

Answer:

$4.5$