Question

David wants to find the height of a building. He places his 353535 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 101010 feet. How tall is the building? Round your answer to the nearest tenth. Click Here for Help Video.





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Answer 1

To find the height of the building using the ladder, we can apply the Pythagorean theorem. According to the theorem, for a right triangle, the sum of the squares of the two shorter sides (base and height) is equal to the square of the longest side (the ladder in this case).

Let's define:
- \( h \) = height of the building (the vertical side of the triangle)
- \( b \) = base of the building (the horizontal side of the triangle) = 10 feet
- \( L \) = length of the ladder (the hypotenuse) = 35 feet

According to the Pythagorean theorem:
\[
L^2 = b^2 + h^2
\]

Substituting the known values:
\[
35^2 = 10^2 + h^2
\]

Calculating the squares:
\[
1225 = 100 + h^2
\]

Now, subtract 100 from both sides:
\[
1225 - 100 = h^2
\]
\[
1125 = h^2
\]

Now, take the square root of both sides to find \( h \):
\[
h = \sqrt{1125}
\]

Calculating \( \sqrt{1125} \):
\[
h \approx 33.541
\]

Rounding to the nearest tenth, we get:
\[
h \approx 33.5
\]

Thus, the height of the building is approximately **33.5 feet**.