A ladder 28 feet long leans against the side of a building, and the angle between the ladder and the building is 23°.

Question

A ladder 28 feet long leans against the side of a building, and the angle between the ladder and the building is 23°.

(a) Approximate the distance from the bottom of the ladder to the building. (Round your answer to two decimal places.)

   ft

(b) If the distance from the bottom of the ladder to the building is increased by 2.0 feet, approximately how far does the top of the ladder move down the building? (Round your answer to two decimal places.)

 ft

Answer 1

top of ladder is 10.94 feet = 28sin23

distance at the ground level or base = 25.77 feet

add 2 to get 27.77

cosA =0.9919

A = the new lower angle = 7.282 degrees

sinA = .12676

new lower height = 3.55 feet

moving the ladder further away by 2 feet lowered the top of it by 7.39 feet (10.94-3.55)

Answer 2

a)

sin 23 = x/28

x = 28*sin23

= 10.940471597699665141738368488895

= 10.94 (rounded to 2 digits)

10 feet 11 and 5/12 inches

b) Again, by pythagorean

28^2 = (12.94)^2 + h^2

h = 24.830553759431141611391843565025

24.83 feet

24 feet 10 in