# functions

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john's paint crew knows from experience that its 18 ft ladder is particularly stable when the distance from the ground to the top of the ladder is 5 ft more than the distance from the building to the base of the ladder. in this position, how far up the building does the ladder reach?

• functions -

Functions?

This is a geometry problem.

The ladder up against the wall forms a right triangle.

x = base
x + 5 = opposite side
18 = hypotenuse

Using the Pythagorean theorem,
x^2 + (5 + x)^2 = 18^2

Solve for x

5 + x = how far up the blding the ladder reaches.

• functions -

let the base be x ft
then the height is x+5 ft

solve x^2 + (x+5)^2 = 18^2

• functions -

14.98?

• functions -

x = 9.989983874

(9.979983874)^2 + (9.979983874 + 5)^2 = 18^2

The height is exactly 14.979983874 ft.

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