a ladder leans against a building so that the base of the ladder makes a 68 degree angle with the ground if the ladder is 15 feet long how far is the base of the ladder to the base of the building?

Answer 1

Draw and label a diagram

d represents the distance from the wall

cos 68° = d / 15

Can you solve for d and answer?

Answer 2

For reference, I'm using the image of a ladder from https://web.njit.edu/~binchen/phys111/LectureNotes/Physics111_lecture12.pdf to aid in my description.

So in the problem, we're given that l, the length of the ladder, is 15ft. Additionally, we're given that the angle θ is 68°. We're trying to find the length from the bottom of the ladder to the base of the building (which we can denote as x), so we're looking for a relationship between x, l, and θ. If we use our basic trigonometry functions (SOHCAHTOA), we know that cos(θ) = x / l.

Since we know two of these three values, we can substitute them in and see that cos(68) = x / 15, so x = 15 * cos(68). If further simplification is needed, we can use a calculator.