Question

A 24-foot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder and the house both sit on level ground.
To the nearest whole number, find the following values:

A. The measure of the angle formed by the base of the ladder and level ground is

B. The measure of the angle formed by the top of the ladder and the second story window is

C. The distance, on level ground, between the base of the ladder and the house is 
feet.

Answer 1

The ladder, leaning against the building, forms a right triangle with height "a" being the distance from the ground to the window, and hypotenuse "c" being the length of the ladder.

Because it's a right triangle, we can use trigonometric ratios to find the angles we're missing.

For part A), to solve for the angle between the base of the ladder and the ground, you'll want to use sine, because we know the lengths of the opposite side and the hypotenuse.

Sin(x) = a/c , solve for angle x in degrees or radians.

For part B), finding the angle between the top of the ladder and the building, remember that the sum of the angles in a triangle is 180 degrees, or pi radians, depending on which unit your teacher prefers.

Assuming degrees, we can say that angle y = 180-90-x. You are simply subtracting the two known angles to find the third.

For part C) use the Pythagorean theorem. You're looking for the length of the base, "b". Recall:

a^2 + b^2 = c^2

Plug in the known values, and solve for b.