Question

Suppose a 13 foot ladder is leaning against a building reaching to the bottom of a second floor window 12feet above the ground what angle in radians does the ladder make with the building?

Answer 1

θ ≈ 1.17600521 rad

Explanation:

Answer 2

Answer: 1.17600521 rad

Explanation:

To find the angle (in radians) that the ladder makes with the building, we can use the right triangle formed by the ladder, the building, and the ground. The ladder acts as the hypotenuse of the right triangle, with a length of 13 feet. The height from the ground to the second-floor window is the side opposite the angle we want to find, which has a length of 12 feet.

We can use the sine function to find the angle, θ:

sin(θ) = opposite side / hypotenuse

sin(θ) = 12 / 13

Now, to find the angle θ in radians, we can use the inverse sine function (arcsin):

θ = arcsin(12/13)

Plug the value into a calculator to get the angle in radians:

θ ≈ 1.17600521 rad