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 integer as needed.)

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the side opposite the angle \(A\) (\(BC = 15\) m) and we want to find the hypotenuse \(c\). We use the sine function since \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(A = 32^{\circ}\) and the opposite side to \(A\) is \(15\) m. So, \(\sin A=\sin32^{\circ}=\frac{15}{c}\).

Step2: Solve for \(c\)

We can rewrite the equation \(\sin32^{\circ}=\frac{15}{c}\) as \(c=\frac{15}{\sin32^{\circ}}\).
We know that \(\sin32^{\circ}\approx0.5299\). Then \(c=\frac{15}{0.5299}\approx28.3\).

Step3: Round to the nearest integer

Rounding \(28.3\) to the nearest integer gives \(c\approx28\).

Answer:

28