Question
A right triangle is shown. The length between the diagonal line, the length between A and B is 9. The length of the slanted line, the length between A and C, is 15. The length between the horizontal line, the length between B and C, is 12. Use the inverse of tangent to solve for the approximate angle measure of vertex C , rounded to the nearest whole degree. (1 point) Responses 39° 39° 59° 59° 53° 53° 37°
Answers
GPT-4o mini
To find the angle measure of vertex C in the right triangle, we can use the tangent function. From the triangle, we know the following lengths:
- AB (opposite side to angle C) = 9
- BC (adjacent side to angle C) = 12
The tangent of angle C can be calculated using the formula:
\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{12} = \frac{3}{4}
\]
Next, we find the angle C using the arctangent (inverse tangent) function:
\[
C = \tan^{-1}\left(\frac{3}{4}\right)
\]
Calculating this gives:
\[
C \approx 36.87°
\]
Rounding to the nearest whole degree, angle C is approximately \(37°\).
Thus, the answer is **37°**.
- AB (opposite side to angle C) = 9
- BC (adjacent side to angle C) = 12
The tangent of angle C can be calculated using the formula:
\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{12} = \frac{3}{4}
\]
Next, we find the angle C using the arctangent (inverse tangent) function:
\[
C = \tan^{-1}\left(\frac{3}{4}\right)
\]
Calculating this gives:
\[
C \approx 36.87°
\]
Rounding to the nearest whole degree, angle C is approximately \(37°\).
Thus, the answer is **37°**.