Answer: 12.84 degrees
Step-by-step explanation: To find the measure of angle B in a right triangle, we can use the trigonometric function of sine, which is defined as the ratio of the opposite side to the hypotenuse. In this case, the hypotenuse is AB, and the opposite side of angle B is AC.
We are given that the hypotenuse AB is 9 units, and the smaller side AC is 2 units. We know that angle C is a right angle, which means it measures 90 degrees.
Using the sine function, we can write:
sin(B) = opposite/hypotenuse = AC/AB = 2/9.
To find the measure of angle B, we can take the inverse sine (arcsin) of both sides:
B = arcsin(2/9)
Using a calculator, we find that B ≈ 12.84 degrees. Rounded to the nearest hundredth, the measure of angle B is approximately 12.84 degrees.
So the final answer is:
∠B ≈ 12.84 degrees