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:

$$\boxed{{\displaystyle 39}}$$

So, the measure of angle $A$ is approximately 39 degrees.