To find the height \( h \) from the given information, we can use basic trigonometry. In this scenario, we can assume that \( a \) represents the length of the base of a right triangle where this angle \( C \) is opposite the height \( h \).
Using the sine function, we can express the relationship as:
\[ \sin(C) = \frac{h}{a} \]
Rearranging the formula to solve for \( h \):
\[ h = a \cdot \sin(C) \]
Given that \( a = 15 \) yards and \( \angle C = 62^\circ \):
-
We first calculate \( \sin(62^\circ) \).
- Using a calculator, we find: \[ \sin(62^\circ) \approx 0.8829 \]
-
Now substitute the values into the equation for \( h \):
\[ h = 15 \cdot \sin(62^\circ) \] \[ h = 15 \cdot 0.8829 \approx 13.2435 \]
- Rounding to the nearest yard, we get:
\[ h \approx 13 \text{ yards} \]
Thus, the measure of \( h \) to the nearest yard is 13 yards.