Question

A ladder that us 20 feet long leans against the outside of a building.The bottom of the ladder is 6 feet away from the wall. which of the following measurements is the best estimate for how far up the building the ladder reaches?

A 21 feet
B 19 feet
C 26 feet
D 14 feet

Answer 1

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

Explanation: