Question
Use the inverse of the tangent ratio to find the approximate measure at angle B. Round your answer to the nearest whole degree.
Imagine a right triangle. The side line is labelled 20, and the bottom line is labelled 25. The top point is point B, the point below it is pint C, and the point to the right of it is point A.
Imagine a right triangle. The side line is labelled 20, and the bottom line is labelled 25. The top point is point B, the point below it is pint C, and the point to the right of it is point A.
Answers
GPT-4o mini
To find the angle \( B \) in a right triangle using the tangent ratio, we can use the inverse tangent function (also known as arctan or tan\(^{-1}\)).
In your triangle:
- The side opposite angle \( B \) (which we will denote as side AC) is 20.
- The side adjacent to angle \( B \) (which we will denote as side AB) is 25.
The tangent of angle \( B \) is given by the ratio of the opposite side to the adjacent side:
\[
\tan(B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{25}
\]
Now, we can find angle \( B \) using the inverse tangent function:
\[
B = \tan^{-1}\left(\frac{20}{25}\right)
\]
Calculating the ratio:
\[
\frac{20}{25} = 0.8
\]
Now, using a calculator to find the inverse tangent:
\[
B \approx \tan^{-1}(0.8)
\]
Using a calculator, we find:
\[
B \approx 38.66 \text{ degrees}
\]
Rounding this to the nearest whole degree, we get:
\[
B \approx 39 \text{ degrees}
\]
Thus, the approximate measure of angle \( B \) is \( \boxed{39} \) degrees.
In your triangle:
- The side opposite angle \( B \) (which we will denote as side AC) is 20.
- The side adjacent to angle \( B \) (which we will denote as side AB) is 25.
The tangent of angle \( B \) is given by the ratio of the opposite side to the adjacent side:
\[
\tan(B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{25}
\]
Now, we can find angle \( B \) using the inverse tangent function:
\[
B = \tan^{-1}\left(\frac{20}{25}\right)
\]
Calculating the ratio:
\[
\frac{20}{25} = 0.8
\]
Now, using a calculator to find the inverse tangent:
\[
B \approx \tan^{-1}(0.8)
\]
Using a calculator, we find:
\[
B \approx 38.66 \text{ degrees}
\]
Rounding this to the nearest whole degree, we get:
\[
B \approx 39 \text{ degrees}
\]
Thus, the approximate measure of angle \( B \) is \( \boxed{39} \) degrees.