Question
If a 15 yards and ∠C= 62 degrees, what is the measure of h to the nearest yard? < (1 point) 28 yards 13 yards 7 yards 16 yards
Answers
GPT-4o mini
To find the height \( h \) using the information provided, we need to use trigonometry. We can assume that the problem describes a right triangle where:
- One of the sides (let's say side \( a \)) is the base (15 yards).
- Angle \( C \) is the angle opposite to the height \( h \).
Since we are trying to find \( h \), we can use the tangent function:
\[
\tan(\angle C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{a}
\]
Here, \( a \) is the length of the adjacent side, which is 15 yards, and \( C = 62^\circ \).
Thus, we can rearrange the equation to solve for \( h \):
\[
h = a \cdot \tan(C) = 15 \cdot \tan(62^\circ)
\]
Now, let's calculate \( h \):
1. Calculate \( \tan(62^\circ) \):
- Using a calculator, \( \tan(62^\circ) \approx 1.8807 \).
2. Now plug this value into the equation:
\[
h \approx 15 \cdot 1.8807 \approx 28.21 \text{ yards}
\]
Rounding to the nearest yard, \( h \approx 28 \) yards.
Thus, the measure of \( h \) to the nearest yard is **28 yards**.
- One of the sides (let's say side \( a \)) is the base (15 yards).
- Angle \( C \) is the angle opposite to the height \( h \).
Since we are trying to find \( h \), we can use the tangent function:
\[
\tan(\angle C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{a}
\]
Here, \( a \) is the length of the adjacent side, which is 15 yards, and \( C = 62^\circ \).
Thus, we can rearrange the equation to solve for \( h \):
\[
h = a \cdot \tan(C) = 15 \cdot \tan(62^\circ)
\]
Now, let's calculate \( h \):
1. Calculate \( \tan(62^\circ) \):
- Using a calculator, \( \tan(62^\circ) \approx 1.8807 \).
2. Now plug this value into the equation:
\[
h \approx 15 \cdot 1.8807 \approx 28.21 \text{ yards}
\]
Rounding to the nearest yard, \( h \approx 28 \) yards.
Thus, the measure of \( h \) to the nearest yard is **28 yards**.