Question

find uv and the area of $\triangle vwx$.
18 m
$70^\circ$
15 m
write your answer as an integer or as a decimal rounded to the nearest tenth.
$uv = \square$ m
area $= \square$ $\text{m}^2$

Explanation:

Step1: Calculate UV using cosine

In right $\triangle XUV$, $\cos(70^\circ)=\frac{UV}{XV}$
$UV = XV \cdot \cos(70^\circ) = 15 \cdot \cos(70^\circ)$
$UV \approx 15 \cdot 0.3420 = 5.13$
Rounded to nearest tenth: $UV \approx 5.1$

Step2: Calculate XU using sine

In right $\triangle XUV$, $\sin(70^\circ)=\frac{XU}{XV}$
$XU = XV \cdot \sin(70^\circ) = 15 \cdot \sin(70^\circ)$
$XU \approx 15 \cdot 0.9397 = 14.0955$

Step3: Calculate area of $\triangle VWX$

Base $XW=18$, height $XU\approx14.0955$
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 18 \times 14.0955$
$\text{Area} = 9 \times 14.0955 \approx 126.86$
Rounded to nearest tenth: $\text{Area} \approx 126.9$

Answer:

$UV = 5.1$ m
$\text{Area} = 126.9$ m²