Question

If h=10 meters and m∠C = 39° , then what is the length of side a? Round your answer to the nearest whole number.

(1 point)
Responses

13 meters
13 meters

16 meters
16 meters

8 meters
8 meters

6 meters
6 meters

Answer 1

To find the length of side \( a \) in a right triangle where \( h = 10 \) meters is the height (or the side opposite to angle \( C \)) and \( m∠C = 39° \), we can use the sine function from trigonometry.

The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse. The formula is:

\[
\sin(C) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case, we have:

\[
\sin(39°) = \frac{h}{a}
\]

Substituting the known values:

\[
\sin(39°) = \frac{10}{a}
\]

Now we can solve for \( a \):

\[
a = \frac{10}{\sin(39°)}
\]

Using a calculator, we find \( \sin(39°) \):

\[
\sin(39°) \approx 0.6293
\]

Then:

\[
a \approx \frac{10}{0.6293} \approx 15.9
\]

Rounding to the nearest whole number gives us:

\[
a \approx 16 \text{ meters}
\]

Therefore, the length of side \( a \) is **16 meters**.