Question

A right triangle is shown. The diagonal line measures 12, the horizontal line measures 5, and the slanted line measures 13. Use the inverse of cosine to find the approximate interior angle measure at vertex A . Round your answer to the nearest whole degree. (1 point) A≈ °

Answer 1

In a right triangle, we can use the cosine function to find an angle when we know the lengths of the sides. Given your triangle, we can identify the sides as follows:

- The horizontal line (adjacent to angle A) is 5.
- The hypotenuse (the diagonal line) is 13.

To find the cosine of angle A, we use the formula:

\[
\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{5}{13}
\]

Next, we use the inverse cosine function to find the angle A:

\[
A \approx \cos^{-1}\left(\frac{5}{13}\right)
\]

Now we can calculate the value using a calculator:

\[
A \approx \cos^{-1}(0.3846) \approx 67.9^\circ
\]

Rounding to the nearest whole degree gives:

\[
A \approx 68^\circ
\]

Thus, the approximate measure of angle A is \( \boxed{68} \) degrees.