A ladder 30 feet long leans against the side of a building, and the angle between the ladder and the building is 22°.

Question

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

(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.)

Answer 1

(a) Then sin(22) = x/30

where x is the measure of the base (from bottom of ladder to wall of building)

30 * sin(22) = x

x = 11.238197802477361062448913235036...

which is approximately 11.24 feet

11 feet 2 and 7/8 inches

ALSO,

cos(22) = h/30, where h is the measure of the top of the ladder to the ground.

Then

h = 30*cos(22) = 27.815515637003622024194233534109

which is approximately 27.82 feet

or 27 feet 9 and 13/16 inches

(b)

The base is now 13.24 feet...

Pythagorean says:

30^2 = 13.24^2 + h^2 where h is the measure of top of ladder to ground

900 = 175.2976 + h^2

h = 26.92

26 feet 11 and 1/16 inches

The difference is: 27.82 - 26.92 = 0.9 feet

or approximately 10 and 13/16 inches

check:

27 feet 9 and 3/16 inches

MINUS

26 feet 11 and 1/16 inches

requires borrowing from the feet measurement...

1 foot = 12 inches

21 and 3/16 - 11 and 1/16 =

10 and 1/8 inches..

This is a discrepency of 1/16 inch caused by roundoff error

The difference is: 27.82 - 26.92 = 0.9 feet

or approximately 10 and 13/16 inches

In summary, the answers are:

a) 11.24 feet

b) 0.9 feet or just over 10 inches