A right triangle has legs of 6 and 7. Angle A is opposite the side labeled 6.

Question

Question
Use the triangle to answer the question.

Find the measure of angle A. Round your answer to the nearest hundredth.
(1 point)
Responses

59.00°
59.00°

49.40°
49.40°

40.60°
40.60°

31.00

Answer 1

To find the measure of angle A in the right triangle, you can use the tangent function, which is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, angle A is opposite the leg of length 6, and the other leg (the adjacent side) has a length of 7.

You can use the following formula:

\[ \tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{7} \]

Now, to find angle A, take the arctangent (inverse tangent) of the ratio:

\[ A = \tan^{-1}\left(\frac{6}{7}\right) \]

Using a calculator to find this value:

\[ A \approx \tan^{-1}(0.8571) \approx 40.60° \]

So, the measure of angle A rounded to the nearest hundredth is approximately 40.60°.