Question
If h = 10 meters and m angle C = 39 degree, then what is the length of side a? Round your answer to the nearest whole number.
a. 16 meters
b. 6 meters
c. 13 meters
d. 8 meters
a. 16 meters
b. 6 meters
c. 13 meters
d. 8 meters
Answers
GPT-4o mini
To find the length of side \( a \) in a triangle where you know the height \( h \) and the angle \( C \), you can use the relationship involving the height and angle.
Assuming we are dealing with a right triangle, the height (h) corresponds to the side opposite angle \( C \), which means:
\[
h = a \cdot \sin(C)
\]
Given that \( h = 10 \) meters and \( C = 39^\circ \):
\[
10 = a \cdot \sin(39^\circ)
\]
First, calculate \( \sin(39^\circ) \):
\[
\sin(39^\circ) \approx 0.6293
\]
Now, substitute and solve for \( a \):
\[
10 = a \cdot 0.6293
\]
Dividing both sides by \( 0.6293 \):
\[
a = \frac{10}{0.6293} \approx 15.9
\]
Rounding this to the nearest whole number gives:
\[
a \approx 16 \text{ meters}
\]
Thus, the length of side \( a \) rounded to the nearest whole number is:
**a. 16 meters**.
Assuming we are dealing with a right triangle, the height (h) corresponds to the side opposite angle \( C \), which means:
\[
h = a \cdot \sin(C)
\]
Given that \( h = 10 \) meters and \( C = 39^\circ \):
\[
10 = a \cdot \sin(39^\circ)
\]
First, calculate \( \sin(39^\circ) \):
\[
\sin(39^\circ) \approx 0.6293
\]
Now, substitute and solve for \( a \):
\[
10 = a \cdot 0.6293
\]
Dividing both sides by \( 0.6293 \):
\[
a = \frac{10}{0.6293} \approx 15.9
\]
Rounding this to the nearest whole number gives:
\[
a \approx 16 \text{ meters}
\]
Thus, the length of side \( a \) rounded to the nearest whole number is:
**a. 16 meters**.