Question

use the image to answer the question
(1 point)
if h = 10 meters and m∠c = 39°, then what is the length of side a? round your answer to the nearest whole number
16 meters
8 meters
13 meters
8 meters

Explanation:

Step1: Identify the trigonometric relation

We have a right - triangle (formed by the height \(h\), side \(a\), and the perpendicular from \(B\) to \(AC\)). In this right - triangle, \(\sin(C)=\frac{h}{a}\) (since \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), where \(\theta = C\), the opposite side to \(\theta\) is \(h\) and the hypotenuse is \(a\)).

Step2: Rearrange the formula to solve for \(a\)

From \(\sin(C)=\frac{h}{a}\), we can rearrange it to get \(a=\frac{h}{\sin(C)}\).

Step3: Substitute the given values

We know that \(h = 10\) meters and \(C=39^{\circ}\). So we substitute these values into the formula: \(a=\frac{10}{\sin(39^{\circ})}\).

We know that \(\sin(39^{\circ})\approx0.6293\). Then \(a=\frac{10}{0.6293}\approx15.89\approx16\) meters.

Answer:

16 meters