Question

Use the inverse of tangent to find the approximate measure of angle A, rounded to the nearest whole degree.
Imagine a right triangle. The slanted line is labelled 13, the bottom line is labelled 12, and the side line is labelled 5. The top point is labelled point A, the point below it is labelled C, and the point to the right of that is labelled B.

Answer 1

In the right triangle you described, we can identify the sides based on their positions. You have:

- The slanted line (hypotenuse) AC = 13
- The bottom line (adjacent side) BC = 12
- The side line (opposite side) AB = 5

To find the measure of angle A (angle CAB), we can use the tangent function. The tangent of angle A is defined as the ratio of the length of the opposite side (AB) to the length of the adjacent side (BC):

\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{AB}{BC} = \frac{5}{12}
\]

Now we can find angle A by taking the inverse tangent (arctangent) of the ratio.

\[
A = \tan^{-1}\left(\frac{5}{12}\right)
\]

Using a calculator to compute this:

\[
A \approx \tan^{-1}(0.4167) \approx 22.6^\circ
\]

Rounding to the nearest whole degree, we get:

\[
A \approx 23^\circ
\]

Thus, the approximate measure of angle A is **23 degrees**.