Question
Use the inverse of tangent to find the approximate measure of angle A , rounded to the nearest whole degree. (1 point) Responses 21° 21° 67° 67° 43° 43° 23° (Angles of the triangles are, 13, 12, and 5)
Answers
GPT-4o mini
To find the angle \( A \) using the inverse of tangent (or arctan), we need to have the lengths of the sides of the triangle involved.
Assuming that you are dealing with a right triangle where sides opposite angle \( A \) is 5 (the side across from angle \( A \)), and the adjacent side to angle \( A \) is 12, you can use the tangent function, which is defined as:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}
\]
To find angle \( A \), you take the inverse tangent:
\[
A = \tan^{-1}\left(\frac{5}{12}\right)
\]
Now, you can calculate this using a calculator:
\[
A \approx \tan^{-1}(0.4167) \approx 22.6°
\]
Rounded to the nearest whole degree, angle \( A \) is approximately \( 23° \).
So, the correct response is **23°**.
Assuming that you are dealing with a right triangle where sides opposite angle \( A \) is 5 (the side across from angle \( A \)), and the adjacent side to angle \( A \) is 12, you can use the tangent function, which is defined as:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}
\]
To find angle \( A \), you take the inverse tangent:
\[
A = \tan^{-1}\left(\frac{5}{12}\right)
\]
Now, you can calculate this using a calculator:
\[
A \approx \tan^{-1}(0.4167) \approx 22.6°
\]
Rounded to the nearest whole degree, angle \( A \) is approximately \( 23° \).
So, the correct response is **23°**.