Question

8
(blue right triangle with angle 31°, hypotenuse v, vertical side 19)
add
1000 more rows at the bottom
answer sheet problems

Explanation:

Step1: Identify trigonometric ratio

For the $31^\circ$ angle, the side of length 19 is the opposite side, and $v$ is the hypotenuse. We use the sine ratio: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(31^\circ)=\frac{19}{v}$

Step2: Rearrange to solve for $v$

Isolate $v$ by cross-multiplying:
$v=\frac{19}{\sin(31^\circ)}$

Step3: Calculate the value

Use $\sin(31^\circ)\approx0.5150$:
$v\approx\frac{19}{0.5150}\approx36.9$

Answer:

$v\approx36.9$