For a given right triangle, side a = 400 feet and side b = 900 feet.What is the measure of angle A to the nearest degree?

24

To find the measure of angle A in a right triangle, you can use the trigonometric function called the inverse tangent (or arctan). The formula to calculate the measure of an angle in a right triangle is:

angle A = arctan(side opposite angle A / side adjacent to angle A)

In this case, side a is opposite to angle A, and side b is adjacent to angle A. So, we can substitute the values into the formula:

angle A = arctan(400/900)

To find the inverse tangent, you can use a scientific calculator or an online calculator with the arctan function. Plugging in the values, we get:

angle A = arctan(400/900) ≈ 24.4 degrees

Therefore, the measure of angle A to the nearest degree is approximately 24 degrees.