To find the measure of angle A in a right triangle where the legs are 6 and 7, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side.
In this case, we want to find angle A, which is opposite to the side with length 6. The other leg (adjacent to angle A) has a length of 7. Therefore, we can set up the following equation using the tangent function:
\[ \tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{7} \]
To find angle A, we take the arctangent (inverse tangent) of the ratio:
\[ A = \tan^{-1}\left(\frac{6}{7}\right) \]
Now, we can calculate this using a calculator:
\[ A \approx \tan^{-1}(0.8571) \approx 40.60° \]
Rounding to the nearest hundredth, angle A is approximately \( 40.60° \).
Therefore, the correct response is 40.60°.