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

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:

\[
\boxed{39^\circ}
\]

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