Question

Use the inverse of tangent to solve for the approximate angle measure of vortex C, rounded to the nearest whole degree.
Imagine a right triangle. The slanted line on top is labelled 15, the bottom line is labelled 12, and the line on the left is labelled 9. The top point is point A, the point below it is point B, and the point to the right of it is point C.

Answer 1

In your right triangle, it seems like we're dealing with vertices A, B, and C, where:

- Side AB (the vertical side) is 9 units,
- Side BC (the horizontal side) is 12 units,
- Side AC (the hypotenuse or slanted side) is 15 units.

To find the angle at point C (denoted as angle ACB), we can use the tangent function:

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

In this case, the opposite side to angle C (which is side AB) is 9, and the adjacent side (which is side BC) is 12. Thus, we can write:

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

Now, we simplify:

\[
\tan(C) = \frac{3}{4}
\]

Next, we use the inverse tangent function (arctan) to find the angle:

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

Calculating this using a calculator, we find:

\[
C \approx 36.87^\circ
\]

Rounding to the nearest whole degree, the approximate measure of angle C is:

\[
\boxed{37^\circ}
\]