10 pts A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the
building. How many feet away from the building is the base of the ladder? Write only the number
rounded to the nearest tenth of a foot.

13.2 ft

Step-by-step explanation:

We are given a ladder, a building, and an angle. Let's construct a right triangle (see attachment).

In this right triangle, we know that the hypotenuse (the ladder) is 25 feet, while the angle made between the top of the ladder and the building is 32°. Since we want to find the number of feet between the building and the base of the ladder, we will use the trigonometric function sine, which is opposite divided by hypotenuse.

Here, the opposite side is the value we want to find, while the hypotenuse is the length of the ladder.

We have:

sin(32°) = opposite / hypotenuse = x / 25

x = 25 * sin(32°) ≈ 13.2 ft

The answer is thus 13.2 ft.

~ an aesthetics lover