SOLUTION: Two ladders are leaning against a wall. The longer ladder is 7.2 ft long. The shorter ladder is 6 ft long. Both ladders are leaning against the wall at the same angle measure. The

Algebra ->  Angles -> SOLUTION: Two ladders are leaning against a wall. The longer ladder is 7.2 ft long. The shorter ladder is 6 ft long. Both ladders are leaning against the wall at the same angle measure. The       Log On


   

Question 1081260: Two ladders are leaning against a wall. The longer ladder is 7.2 ft long. The shorter ladder is 6 ft long. Both ladders are leaning against the wall at the same angle measure. The base of the smaller ladder is 2.5 ft from the base of the wall.
How far away is the base of the longer ladder to the base of the wall?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two ladders are leaning against a wall.
The longer ladder is 7.2 ft long. The shorter ladder is 6 ft long.
Both ladders are leaning against the wall at the same angle measure.
The base of the smaller ladder is 2.5 ft from the base of the wall.
How far away is the base of the longer ladder to the base of the wall?
:
let x = the distance the longer ladder base is from the smaller ladder
then
(x+2.5) = the distance the longer ladder is from the wall
:
Both angles have the same cosine (side adjacent/hypotenuse)
%28%28x%2B2.5%29%29%2F7.2 = 2.5%2F6
cross multiply
6(x+2.5) = 7.2 * 2.5
6x + 15 = 18
6x = 18 - 15
6x = 3
x = 3/6
x = .5 ft
the longer ladder: 2.5 + .5 = 3 ft from wall