How long is a ladder whose base is 3 ft from a wall and makes an 80° angle with the ground?

Question 15 options:

10 ft


12 ft


14 ft


17 ft

Basic trig,

if the length of the ladder is h ft

3/h = cos 80°
h = 3/cos80° = appr 17 ft

To find the length of the ladder, we can use trigonometry. Specifically, we can use the trigonometric function cosine (cos) because we have the adjacent side (the distance of the base of the ladder from the wall) and the angle.

First, let's draw a right triangle to visualize the problem. The base of the ladder is one side of the right triangle, the wall is the other side, and the ladder itself is the hypotenuse.

Next, look at the given angle, which is 80°. The adjacent side is the base of the ladder, which is 3 ft. The cosine function is defined as the ratio of the adjacent side to the hypotenuse.

Using the cosine function, we can determine the length of the ladder.
Cos(80°) = Adjacent / Hypotenuse
Cos(80°) = 3 ft / Hypotenuse

Now, we can solve for the length of the ladder:
Hypotenuse = 3 ft / Cos(80°)

Using a calculator, we can find the value of Cos(80°), which is approximately 0.1736.
Hypotenuse = 3 ft / 0.1736
Hypotenuse ≈ 17.27 ft

Therefore, the length of the ladder is approximately 17.27 ft.

Comparing this result to the options given, the closest option is 17 ft.