Question
If \( a=15 \) yards and \( \angle C=62 \) degrees, what is the measure of \( h \) to the nearest yard? (1 point)
Ask by Little Edwards. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( h \approx 13 \) yards
Solution
To find the height \( h \) relative to side \( a \) in a triangle, you can use the sine function:
\[
h = a \times \sin(\angle C)
\]
Given:
- \( a = 15 \) yards
- \( \angle C = 62^\circ \)
Calculating:
\[
h = 15 \times \sin(62^\circ) \approx 15 \times 0.8829 \approx 13.244 \text{ yards}
\]
Rounding to the nearest yard:
\[
h \approx 13 \text{ yards}
\]
**Answer:** 13 yards
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the height \( h \), we can use the sine function in a right triangle, where \( h \) is the side opposite \( \angle C \), and \( a \) (the length of the adjacent side) is 15 yards. We use the formula: \[ h = a \cdot \sin(\angle C) \] Plugging in the values: \[ h = 15 \cdot \sin(62^\circ) \] Calculating \( \sin(62^\circ) \) (approximately 0.8746): \[ h \approx 15 \cdot 0.8746 \approx 13.12 \] Rounding \( h \) to the nearest yard gives: \[ h \approx 13 \text{ yards} \] So, the measure of \( h \) to the nearest yard is 13 yards.
