Question

Area of Triangles Quick Check 2 of 52 of 5 Items Question Use the image to answer the 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 8 meters 8 meters 16 meters 16 meters 13 meters 13 meters 6 meters 6 meters Skip to navigation page 14 of 14

Answer 1

To find the length of side \( a \) in a triangle where you know the height \( h \) and the angle \( m∠C \), we can use trigonometric functions. In this case, we can apply the sine function since we have an angle and the opposite side (height).

Given:
- \( h = 10 \) meters (this is the height from point A to side a)
- \( m∠C = 39° \)

From trigonometry, the sine of angle \( C \) is defined as the ratio of the opposite side to the hypotenuse. In this scenario, you can compute the length of side \( a \) as follows:

\[
\sin(39°) = \frac{h}{a}
\]

Rearranging the equation to solve for \( a \):

\[
a = \frac{h}{\sin(39°)}
\]

Plugging in the height value:

\[
a = \frac{10}{\sin(39°)}
\]

Now, calculate \( \sin(39°) \):

Using a calculator:

\[
\sin(39°) \approx 0.6293
\]

Now substitute this into the equation for \( a \):

\[
a \approx \frac{10}{0.6293} \approx 15.9 \, \text{meters}
\]

Now, round this to the nearest whole number:

Thus, \( a \approx 16 \) meters.

**Final Answer: 16 meters**.