Question

Find the measure of angle A. Round your answer to the nearest whole number. No hypotenuse, Adjacent = 25, Opposite = 20

Answer 1

To find the measure of angle \( A \) in a right triangle where the adjacent side is 25 and the opposite side is 20, we can use the tangent function:

\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{25}
\]

Simplifying this gives:

\[
\tan(A) = \frac{4}{5}
\]

Now, to find angle \( A \), we take the arctangent (inverse tangent) of \( \frac{4}{5} \):

\[
A = \tan^{-1}\left(\frac{4}{5}\right)
\]

Using a calculator to compute this:

\[
A \approx 38.66 \text{ degrees}
\]

Rounding to the nearest whole number, we find:

\[
\boxed{39}
\]

So, the measure of angle \( A \) is approximately 39 degrees.