Question

find the measure of the side of the right triangle whose length is designated by the lower case letter c.

c ≈ □ m (round to the nearest whole number.)

Explanation:

Step1: Identify trigonometric ratio

We have angle $A=31^\circ$, opposite side $BC=17$ m, hypotenuse $c$. Use sine: $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(31^\circ)=\frac{17}{c}$

Step3: Solve for c

Rearrange to $c=\frac{17}{\sin(31^\circ)}$. Calculate $\sin(31^\circ)\approx0.5150$, so $c\approx\frac{17}{0.5150}$

Step4: Compute and round

$c\approx33.01$，round to whole number.

Answer:

$33$