A ladder 29 feet long leans against the side of a building, and the angle between the ladder and the building is 23°.

Question

A ladder 29 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

(a)

then sin(23) = x/29 where x is the measure

from the base of the ladder to the building..

x = sin(23)*29 = 11.331202726188938896800453077784

= 11 feet 4 inches is the APPROXIMATION

= 11 + 1/3 feet

= 34/3 feet

(b) Then the base of the ladder is 13 + 1/3 feet

= 40/3 feet from the building

Pythagorean says:

29^2 = (40/3)^2 + h^2 where h is the measure

of the top of the ladder to the ground

841 = 1600/9 + h^2

7569 = 1600 + 9 h^2 <--- multiplies by 9

5969 = 9 h^2

5969/9 = h^2

663 + 2/9 = h^2

h = 25.7531012156....

25 feet 9 + 1/16 inches