Question

find vx and the area of $\triangle uvw$.

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

$vx = \square$ cm

area $= \square$ $\text{cm}^2$

Explanation:

Step1: Calculate length of VX

In right triangle $\triangle UX V$, $\sin(35^\circ) = \frac{VX}{UV}$
$VX = UV \times \sin(35^\circ) = 19 \times \sin(35^\circ)$
Using $\sin(35^\circ) \approx 0.5736$, we get $VX \approx 19 \times 0.5736 \approx 10.9$

Step2: Calculate area of $\triangle UVW$

Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times UW \times VX$
Substitute $UW=42$ and $VX \approx 10.9$:
$\text{Area} = \frac{1}{2} \times 42 \times 10.9 = 21 \times 10.9 = 228.9$

Answer:

$VX = 10.9$ cm
$\text{Area} = 228.9$ cm$^2$