Question
If h =10 meters and m angle C=39 degrees, then what is the length of side a? Round your answer to the nearest whole number.
6 meters
8 meters
13 meters
16 meters
6 meters
8 meters
13 meters
16 meters
Answers
GPT-4o mini
To find the length of side \( a \) in a triangle, you can use the sine function based on the information given. It sounds like we have a right triangle where \( h \) is the height related to angle \( C \) opposite side \( a \).
The relationship can be expressed using the sine of angle \( C \):
\[
\sin(C) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{a}{h}
\]
In this case, we know:
- \( h = 10 \) meters (the hypotenuse)
- \( C = 39^\circ \)
Rearranging the sine formula to solve for \( a \):
\[
a = h \cdot \sin(C)
\]
Substituting the values:
\[
a = 10 \cdot \sin(39^\circ)
\]
Using a calculator to find \( \sin(39^\circ) \):
\[
\sin(39^\circ) \approx 0.6293
\]
Now calculating \( a \):
\[
a = 10 \cdot 0.6293 \approx 6.293
\]
Rounding to the nearest whole number, we get:
\[
a \approx 6
\]
Thus, the length of side \( a \) is **6 meters**.
The relationship can be expressed using the sine of angle \( C \):
\[
\sin(C) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{a}{h}
\]
In this case, we know:
- \( h = 10 \) meters (the hypotenuse)
- \( C = 39^\circ \)
Rearranging the sine formula to solve for \( a \):
\[
a = h \cdot \sin(C)
\]
Substituting the values:
\[
a = 10 \cdot \sin(39^\circ)
\]
Using a calculator to find \( \sin(39^\circ) \):
\[
\sin(39^\circ) \approx 0.6293
\]
Now calculating \( a \):
\[
a = 10 \cdot 0.6293 \approx 6.293
\]
Rounding to the nearest whole number, we get:
\[
a \approx 6
\]
Thus, the length of side \( a \) is **6 meters**.