If a = 6 and c = 15, what is the measure of ∠A? (round to the nearest tenth of a degree) Q: A: A) 21.8° B) 22.7° C) 23.6° D) 66.4°

To find the measure of ∠A given the side lengths a and c of a triangle, we're likely dealing with a right-angled triangle where we can use trigonometric ratios to find the angles. However, without additional context (like which side is the hypotenuse in case of a right triangle or which angle is opposite of which side), we cannot definitively determine the angle measure.

Given the usual convention in a right triangle where side a is opposite angle A and c is the hypotenuse, we can use the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse:

sin(A) = a / c

Plugging in the values we have:

sin(A) = 6 / 15

Now, we need to find the value of angle A:

sin(A) = 0.4

To find the measure of angle A, take the inverse sine (also known as arcsine) of 0.4:

A = arcsin(0.4)

Using a scientific calculator or an online tool to compute this, you'll find that:

A ≈ 23.6 degrees (to the nearest tenth of a degree).

Therefore, the answer is C) 23.6°.