Question

Use the inverse of the tangent ratio to find the approximate measure of angle B . Round your answer to the nearest whole degree. (1 point)
The side between B and C is 20, side between C and A is 25
Angle C is a right angle

Answer 1

To find the measure of angle \( B \) in the right triangle defined by points A, B, and C, we can use the inverse tangent (arctan) function.

In right triangle ABC, where angle C is a right angle, you have:

- The side opposite angle B (BC) = 20 (the side between B and C)
- The side adjacent to angle B (AC) = 25 (the side between C and A)

The tangent of angle B is given by the ratio of the opposite side to the adjacent side:

\[
\tan(B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AC} = \frac{20}{25}
\]

Now, we can simplify this fraction:

\[
\tan(B) = \frac{20}{25} = \frac{4}{5}
\]

Next, we will use the inverse tangent to find angle \( B \):

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

Using a calculator to find \( B \):

\[
B \approx 38.66^\circ
\]

Rounding \( B \) to the nearest whole degree:

\[
B \approx 39^\circ
\]

Thus, the approximate measure of angle \( B \) is \( \boxed{39} \) degrees.