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.
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