Question

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

Explanation:

Step1: Identify trigonometric ratio

In right triangle $VWU$, $\angle U = 47^\circ$, $WU = \sqrt{33}$, and $VW$ is the opposite side to $\angle U$, $WU$ is the adjacent side. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

Let $VW = x$. Substitute $\theta = 47^\circ$, adjacent $= \sqrt{33}$:
$\tan(47^\circ) = \frac{x}{\sqrt{33}}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = \sqrt{33} \times \tan(47^\circ)$
Calculate $\sqrt{33} \approx 5.7446$, $\tan(47^\circ) \approx 1.0724$:
$x \approx 5.7446 \times 1.0724 \approx 6.16$

Step4: Round to nearest tenth

Round $6.16$ to the nearest tenth:
$x \approx 6.2$

Answer:

$VW = 6.2$