Question

A right triangle labeled ABC measurements are 15 for the hypotenuse, 12 for the adjacent leg and the opposite leg is 9. B is at the right angle and A is between the opposite leg and the hypotenuse and c is between the hypotenuse and the adjacent leg.

Use inverse of tangent to solve for the approximate angle measure of vertex C, rounded to the nearest whole degree.
A. 39 degrees
B. 53 degrees
C. 59 degrees
D. 37 degrees

Answer 1

To find the angle measure of vertex C in triangle ABC, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle.

In triangle ABC:
- The side opposite angle C (the opposite leg) = 9
- The side adjacent to angle C (the adjacent leg) = 12

We can use the inverse tangent function (arctan) to find angle C.

The formula we will use is:

\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{12}
\]

Now, we find angle C:

\[
C = \tan^{-1}\left(\frac{9}{12}\right)
\]

Calculating \(\frac{9}{12}\):

\[
\frac{9}{12} = 0.75
\]

Now we find the angle:

\[
C = \tan^{-1}(0.75)
\]

Using a calculator for \(\tan^{-1}(0.75)\):

\[
C \approx 36.87 \text{ degrees}
\]

Rounding to the nearest whole degree gives us:

\[
C \approx 37 \text{ degrees}
\]

Thus, the answer is:

**D. 37 degrees**