Question

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A 24-foot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder and the house both sit on level ground.

To the nearest whole number, find the following values:

A. The measure of the angle formed by the base of the ladder and level ground is ___


B. The measure of the angle formed by the top of the ladder and the second story window is ___


C. The distance, on level ground, between the base of the ladder and the house is ___

Answer 1

a. The angle formed with the ground would be calculated using sin x = 20/24.
sin^-1(20/24) = 56 degrees.
b. The angle formed with the house would be calculated using cos y = 20/24.
cos^-1 (20/24) = 34 degrees.
c. The distance the ladder was placed from the house can be calculated using Pythagorean Theorem or Cos 56 = b/24.
24cos56 = b. b = 13

Answer 2

A. 56.40°

B. 33.59°

C. 13.25 feet

Explanation:

In the given triangle ABC, AB is the height of window at second floor,

AC is ladder and BC is the ground.

A. In this part we have to measure angle C.

Since Sin c =
`(AB)/(AC)`

Sin c =
`(20)/(24)` =
`(5)/(6)` = (0.833)

c = (56.40)°

B. In this part of the question we have to find angle A.

Since Cos A =
`(20)/(24)=(5)/(6)` = (0.833)

A = 33.59°

C. In this part we have to find distance BC.

Since Tan c =
`(AB)/(BC)`

Tan (56.40) =
`(20)/(BC)`

BC =
`(20)/((1.51))= 13.25 feet.`