Question

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

Explanation:

Step1: Identify adjacent side/hypotenuse

In right $\triangle VWU$, $\angle V=64^\circ$, hypotenuse $VU=8.9$, $VW$ is adjacent to $\angle V$.

Step2: Use cosine function

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(64^\circ)=\frac{VW}{8.9}$

Step3: Solve for VW

Rearrange to isolate $VW$: $VW=8.9\times\cos(64^\circ)$
Calculate $\cos(64^\circ)\approx0.4384$, then $VW\approx8.9\times0.4384$

Step4: Compute final value

$8.9\times0.4384\approx3.9$

Answer:

$3.9$