If tan A = (7/2), then which of the following is closest to the measure of

The option which is the closest to the measure of ∠A is 74°

Step-by-step explanation:

The question is answered using the options provided by a similar question from an online source

When tan A = (7/2), we have;

The trigonometric ratio for the tangent of an angle is given as follows;

tan A = (7/2) = 3.5

sin(30°) = 1/2, cos(30°) = (√3/2)

sin(60°) = (√3/2), cos(60°) = (1/2)

sin(45°) = cos(45°) = (√2/2)

tan(30°) = (1/2)/(√3/2) = (√3)/3

tan(45°) = 1

tan(60°) = (√3/2)/(1/2) = √3

The tangent of an angle is increasing as we move from 0° to 90°

Therefore, given that tan A = 7/2 > tan 60° = √3, we have;

∠A > 60°

The option (the options obtained from an online source are; 15°, 39°, 58°, and 74°) which is the closest to the measure of ∠A is 74°.