Question

If the ladder is 24 feet and it touches the building at a vertical distance 16 feet from the ground, what is the angle of elevation the ladder makes with the ground?

a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees

Answer 1

Using the sine function and the given lengths of the ladder and the vertical distance, the angle of elevation is found to be approximately 41.8 degrees, which does not match any of the answer choices provided.

Step-by-step explanation:

To determine the angle of elevation the ladder makes with the ground, we can use trigonometry, specifically the sine function, since we have the opposite side (vertical distance from the ground) and the hypotenuse (length of the ladder). The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

So, we can set up the equation:

sin(angle) = opposite / hypotenuse

= 16 feet / 24 feet

sin(angle) = 2/3

By using the inverse sine function, we find:

angle = sin-1(2/3)

angle ≈ 41.8 degrees

However, since 41.8 degrees is not one of the options provided, it appears there may be an error in the question or the options given. The provided answer choices do not include 41.8 degrees. The closest answer from the options would be option (b) 45 degrees, but it is not the exact answer.