Answer: Let's use the trigonometric ratio of sine to find the measure of the larger acute angle of the right triangle. We have:
sin(theta) = opposite / hypotenuse
where theta is the measure of the larger acute angle, and opposite is the length of the shorter leg of the right triangle. Substituting the given values, we get:
sin(theta) = 2sqrt(6) / 2sqrt(15)
= sqrt(2/5)
Using a calculator, we can find the value of theta to the nearest tenth of a degree:
theta = arcsin(sqrt(2/5))
≈ 38.2°
Therefore, the measure of the larger acute angle of the right triangle is approximately 38.2 degrees.
Explanation: