Question

Find the approximate angle measure of ∠B
. Round your answer to the nearest whole degree.
side are 20 and 25 the long side has no numbers and also has a right angle


(5 points)
Responses

37 degrees
37 degrees

51 degrees
51 degrees

53 degrees

Answer 1

To find the approximate angle measure of ∠B in a right triangle where the sides adjacent to ∠B are 20 (adjacent side) and 25 (hypotenuse), we can use the cosine function.

The cosine of an angle in a right triangle is defined as:

\[
\cos(B) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]

In this case:

\[
\cos(B) = \frac{20}{25}
\]

Calculating that,

\[
\cos(B) = 0.8
\]

Next, we can find the angle B by taking the inverse cosine (arccos):

\[
B = \cos^{-1}(0.8)
\]

Using a calculator:

\[
B \approx 36.87^\circ
\]

Rounding to the nearest whole degree, we get:

\[
B \approx 37^\circ
\]

So the approximate angle measure of ∠B is **37 degrees**.