A ladder is leaning against an 18 ft building. The bottom of the ladder is 8.5 ft from the building. Approximately how tall is the ladder?


The problem involves a right triangle, with height equal to the building’s height, base equal to the distance of the ladder from the building, and diagonal or hypotenuse equal to the length of the ladder.
Height = h = 18 feet
Base = b = 8.5 feet
Hypotenuse = H = ? For right triangles, there is a special formula for this:
The square of the height + the square for the base = the square of the hypotenuse
\(H^{2} = h^{2} + b^{2} = 18^{2} + 8.5^{2} = 324 + 72.25 = 396.25\)
\(H^{2} = 396.25\)
Square root of \(H^{2}\) = square root of 396.25
H = 19.9 feet = Length of the ladder
TIP: It’s easy to arrive at the answer \(H^{2} = 396.25\), but not as easy looking for the square root of 396. Since you will be computing manually, review the answer choices and eliminate the unlikely answers. 396 is definitely not the answer because the square root of 396.25 will be a much smaller number. 40 is also out because if you square it, it is \(40\times 40=1600\). 18 is also eliminated because \(18 \times18=324\) Checking out 20, it is the best answer because \(20\times 20=400\), very close to 396.25.

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