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Question

A right triangle upper A upper B upper C. The right angle, labeled upper C, is on the bottom left. The hypotenuse, side upper A upper B, slopes downward from right to left. All sides are assigned values.
A=5
B=12
C=13

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°
43°

Answer 1

To find the measure of angle A in the right triangle, we can use the definition of the tangent function, which is the ratio of the opposite side to the adjacent side. In this case:

• The side opposite angle A is side B (12).
• The side adjacent to angle A is side A (5).

We can find the tangent of angle A using the formula:

\[ \tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{B}{A} = \frac{12}{5} \]

Next, we use the inverse tangent function to find angle A:

\[ A = \tan^{-1}\left(\frac{12}{5}\right) \]

Calculating \( \frac{12}{5} \) gives us 2.4. Now we can find \( \tan^{-1}(2.4) \) using a calculator:

\[ A \approx 67.38^\circ \]

Rounding to the nearest whole degree, angle A is approximately 67°.

So the correct answer is:

67°.