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 trigonometric ratio

In right triangle \(ABC\), \(\angle C = 90^\circ\), \(\angle A = 40^\circ\), and side \(BC = 22\) m (opposite to \(\angle A\)), side \(c\) (hypotenuse \(AB\)) is to be found. We use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(40^\circ)=\frac{22}{c}\).

Step2: Solve for \(c\)

Rearrange the formula: \(c = \frac{22}{\sin(40^\circ)}\). Calculate \(\sin(40^\circ)\approx0.6428\). Then \(c=\frac{22}{0.6428}\approx34.22\). Round to nearest integer.

Answer:

\(34\)