To find the height \( h \) given one side of a triangle and an angle, we can use the sine function from trigonometry.
Assuming you are working with a right triangle where:
- \( C \) is the angle opposite the height \( h \),
- the side measuring 15 yards is the side adjacent to angle \( C \) (i.e., it's the base of the triangle).
The relationship is given by the sine function:
\[ \sin(C) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \( C = 62^\circ \), and \( \text{opposite} = h \), \( \text{adjacent} = 15 \). However, to use the sine function correctly, we actually find \( h \) using the relation of the opposite side to the hypotenuse:
First, we find the length of the hypotenuse using the cosine function:
\[ \cos(62^\circ) = \frac{15}{\text{hypotenuse}} \]
Rearranging gives us:
\[ \text{hypotenuse} = \frac{15}{\cos(62^\circ)} \]
Now, calculate \( \cos(62^\circ) \):
\[ \cos(62^\circ) \approx 0.4695 \]
So:
\[ \text{hypotenuse} \approx \frac{15}{0.4695} \approx 31.95 \text{ yards} \]
Next, we can find \( h \) using:
\[ h = \text{hypotenuse} \times \sin(62^\circ) \]
Calculating \( \sin(62^\circ) \):
\[ \sin(62^\circ) \approx 0.8746 \]
Now, substituting the values to find \( h \):
\[ h \approx 31.95 \times 0.8746 \approx 27.94 \text{ yards} \]
Thus, rounding to the nearest yard, we find:
\[ h \approx 28 \text{ yards} \]
So, the answer is:
28 yards
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