A 22-foot ladder leaning against the side of a house makes a 77° angle with the ground (see figure).How far up the side of the house does the ladder reach? Round your answer to four decimal places.
A) 21.4361 feet
B) 22.5787 feet
C) 4.9489 feet
D) 5.0791 feet
E) 97.7991 feet

Question

A 22-foot ladder leaning against the side of a house makes a 77° angle with the ground (see figure).How far up the side of the house does the ladder reach? Round your answer to four decimal places. ​  ​  ​
A) 21.4361 feet 
B) 22.5787 feet 
C) 4.9489 feet 
D) 5.0791 feet 
E) 97.7991 feet

Quizplus · Accepted Answer

We can use trigonometric ratios to find the height of the ladder on the house. The sine of the angle is equal to the opposite side (height of the ladder) divided by the hypotenuse (the length of the ladder).

sin(77°) = opposite/hypotenuse
sin(77°) = h/22   (where h is the height)

Solving for h, we get:

h = sin(77°) * 22
h ≈ 21.4361 feet

Therefore, the ladder reaches approximately 21.4361 feet up the side of the house. The best choice is A.

A 22-Foot Ladder Leaning Against the Side of a House