Question

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

Explanation:

Step1: Identify adjacent side, hypotenuse

In right $\triangle UVW$, $\angle V=27^\circ$, adjacent side to $\angle V$ is $UV=8$, hypotenuse is $VW$.

Step2: Use cosine definition

Cosine of angle = $\frac{\text{adjacent}}{\text{hypotenuse}}$, so:
$\cos(27^\circ) = \frac{UV}{VW}$

Step3: Rearrange to solve for VW

Rearrange formula to isolate $VW$:
$VW = \frac{UV}{\cos(27^\circ)}$

Step4: Calculate the value

Substitute $UV=8$ and $\cos(27^\circ)\approx0.8910$:
$VW = \frac{8}{0.8910} \approx 8.989$
Round to nearest tenth: $VW\approx9.0$

Answer:

$VW = 9.0$