Question
Use the inverse of the tangent ratio to find the approximate angle measure at vertex A . Round your answer to the nearest whole degree. (1 point) The angle at vertex A is approximately
The side between B and C is 20, side between C and A is 25
Angle C is a right angle
The side between B and C is 20, side between C and A is 25
Angle C is a right angle
Answers
GPT-4o mini
To find the angle at vertex A using the inverse tangent ratio, we can use the sides of the triangle. Since angle C is a right angle, we can identify the sides relative to angle A.
Given:
- BC = 20 (opposite side to angle A)
- CA = 25 (adjacent side to angle A)
We can use the tangent ratio:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{CA}
\]
Substituting the given values:
\[
\tan(A) = \frac{20}{25} = 0.8
\]
Now we will use the inverse tangent (arctan) to find the angle A:
\[
A \approx \tan^{-1}(0.8)
\]
Using a calculator to find the inverse tangent, we get:
\[
A \approx 38.66^\circ
\]
Rounding to the nearest whole degree, the angle at vertex A is approximately:
\[
\boxed{39^\circ}
\]
Given:
- BC = 20 (opposite side to angle A)
- CA = 25 (adjacent side to angle A)
We can use the tangent ratio:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{CA}
\]
Substituting the given values:
\[
\tan(A) = \frac{20}{25} = 0.8
\]
Now we will use the inverse tangent (arctan) to find the angle A:
\[
A \approx \tan^{-1}(0.8)
\]
Using a calculator to find the inverse tangent, we get:
\[
A \approx 38.66^\circ
\]
Rounding to the nearest whole degree, the angle at vertex A is approximately:
\[
\boxed{39^\circ}
\]