A 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 16-feet high, how far away from the base of the building is the bottom of the ladder located?

Question

Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the exact answer.

Answer 1

| \

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b| \ c

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| ____\

a

a is the ground, b is the building, and c is the ladder

The ladder forms a right triangle with the building and the ground, since the ground is perpendicular to the building

Therefore, we can use the Pythagorean theorem:

c² = a² + b²

From the information in the problem, c is 20 ft, b is 16 ft, and a is what we solve for:

(20 ft)² = a² + (16 ft)²

a = √((20 ft)² - (16 ft)²) = 12 ft

An alternative way to solve this problem is to recognize that 20 and 16 are in the right ratios for a pythagorean triple (3, 4, 5 triangle).

Using this knowledge, we can set the ratios equal to each other:

a/c = 3/5

With c = 20 ft,

a = (3/5)*20 ft = 12 ft

Answer 2