Question

B 20 C 25 A Use the inverse of the tangent ratio to find the approximate angle measure at vertex B Round your answer to the nearest whole degree (1 point)

Answer 1

To find the angle at vertex B using the inverse tangent (also known as arctan), you can use the tangent ratio defined as:

\[
\tan(B) = \frac{\text{opposite}}{\text{adjacent}}
\]

From your values, we have:

- Opposite side (to angle B) = A = 20
- Adjacent side (to angle B) = C = 25

So we can calculate the tangent of angle B as follows:

\[
\tan(B) = \frac{20}{25} = 0.8
\]

Now, to find angle B, we use the arctan function:

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

Using a calculator:

\[
B \approx 38.66^\circ
\]

Rounding to the nearest whole degree, we get:

\[
B \approx 39^\circ
\]

Thus, the approximate angle measure at vertex B is **39 degrees**.