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Question

A right triangle upper A upper B upper C. The right angle, labeled B, is on the bottom left. The hypotenuse, side upper A upper C, slopes downward left to right. All sides are assigned values.

Use the inverse of tangent to solve for the approximate angle measure of vertex C , rounded to the nearest whole degree.
A=9
B=12
C=15

(1 point)
Responses

53°
53°

37°
37°

39°
39°

59°

Answer 1

To find the measure of angle \( C \) in the right triangle \( ABC \), where \( B \) is the right angle, we can use the formula for the tangent of angle \( C \):

\[ \tan(C) = \frac{\text{opposite}}{\text{adjacent}} \]

In this triangle, the side opposite angle \( C \) is side \( AB \) (which has length 9), and the adjacent side is \( BC \) (which has length 12). Thus we have:

\[ \tan(C) = \frac{AB}{BC} = \frac{9}{12} = \frac{3}{4} \]

Now, to find angle \( C \), we take the inverse tangent (arctangent) of \( \frac{3}{4} \):

\[ C = \tan^{-1}\left(\frac{3}{4}\right) \]

Calculating this using a calculator or trigonometric tables:

\[ C \approx 36.87° \]

Rounding to the nearest whole degree gives us:

\[ C \approx 37° \]

Thus, the approximate angle measure of vertex \( C \) is:

37°