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

1 answer

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:

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