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A 26 foot ladder reaches a window that is 24 feet ablve the ground How far us the bottom of the ladder from the base of the house?
Wiki User
∙ 14y ago
50
Emilia Morissette
Wiki User
∙ 14y ago10 feet
Explanation
Think of this as a right triangle with the base being the distance between the bottom of the ladder and the bottom of the side of the house (let a represent this distance). The other base is the distance from the bottom of the house to the window (24 ft) and the hypotenuse is the length of the ladder (26 feet). By the Pythagorean theorem,
a2 + 242 = 262. Solving for a, we get:
a2 + 242 = 262
a2 = 262-242 =676-576=100
a=sqrt(100)=10
[If you are familiar with some basic integral right triangles, you could also notice, without doing the math, that this is similar -- in the geometry sense -- to a 5, 12, 13 right triangle. Once you see that the hypotenuse of a right triangle is 13*k and one base of the triangle is 12*k, you know that the other base is 5*k. In this case, k is clearly 2.]
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