Question

If a=15 yards
and ∠C=62 degrees
, what is the measure of h to the nearest yard?

(1 point)
Responses

28 yards
28 yards

7 yards
7 yards

16 yards
16 yards

13 yards

Answer 1

To find the measure of \( h \), which appears to be the height in a right triangle where \( a \) is the length of the adjacent side and \( \angle C \) is the angle at one of the vertices, we can use the tangent function.

The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. Thus, we can write:

\[
\tan(\angle C) = \frac{h}{a}
\]

Rearranging gives us:

\[
h = a \cdot \tan(\angle C)
\]

Substituting the values we have:

- \( a = 15 \) yards
- \( \angle C = 62^{\circ} \)

Now we need to calculate:

\[
h = 15 \cdot \tan(62^{\circ})
\]

Using a calculator to find \( \tan(62^{\circ}) \):

\[
\tan(62^{\circ}) \approx 1.8807
\]

Now multiply:

\[
h = 15 \cdot 1.8807 \approx 28.11
\]

Rounding this to the nearest yard gives us:

\[
h \approx 28 \text{ yards}
\]

Thus, the answer is:

**28 yards**.