Question
A right triangle is shown. The length between the diagonal side, between A and C is 5. The length between the slanted side, between A and B is 13. And the length between the horizontal line, between C and B is 12.Use the inverse of tangent to find the approximate measure of angle A , rounded to the nearest whole degree. (1 point) Responses 21° 21° 23° 23° 67° 67° 43°
Answers
GPT-4o mini
To find the measure of angle A using the inverse tangent function, we can use the lengths given in the triangle.
In a right triangle, the tangent of an angle is given by the ratio of the length of the opposite side to the length of the adjacent side. In this case:
- The length of the side opposite angle A (which is segment BC) is 12.
- The length of the adjacent side (which is segment AB) is 5.
To find angle A, we can use the formula:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AC} = \frac{12}{5}
\]
Now, we can use the inverse tangent function:
\[
A = \tan^{-1}\left(\frac{12}{5}\right)
\]
Calculating this gives:
\[
A \approx \tan^{-1}(2.4)
\]
Using a calculator:
\[
A \approx 67.38°
\]
Rounded to the nearest whole degree, angle A is approximately \(67°\).
So the answer is \(67°\).
In a right triangle, the tangent of an angle is given by the ratio of the length of the opposite side to the length of the adjacent side. In this case:
- The length of the side opposite angle A (which is segment BC) is 12.
- The length of the adjacent side (which is segment AB) is 5.
To find angle A, we can use the formula:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AC} = \frac{12}{5}
\]
Now, we can use the inverse tangent function:
\[
A = \tan^{-1}\left(\frac{12}{5}\right)
\]
Calculating this gives:
\[
A \approx \tan^{-1}(2.4)
\]
Using a calculator:
\[
A \approx 67.38°
\]
Rounded to the nearest whole degree, angle A is approximately \(67°\).
So the answer is \(67°\).