Answer:
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: