Question

The base of a 15 foot ladder is 6 feet from a building. If the ladder reaches the flat roof, how tall is the building?

Answer 1

13.75 foot

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Use Pythagoras theorem where hypotenuse is 15 feet and base is 6 feet.

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Let the length of building be h.

a² + b² = c²

h² + 6² = 15²

h² + 36 = 225

h² = 225 - 36

h² = 189

h = √189

h = 3√21

h ≈ 13.75 foot

Answer 2

`\rm 3√(21)\approx 13.75\:\:ft\:\:(nearest\:hundredth)`

Explanation:

The given scenario can be modeled as a right triangle, where the distance from the foot of the ladder to the base of the building is the base of the triangle, and the ladder is the hypotenuse of the triangle.

To find the height of the building, and therefore the height of the triangle, use Pythagoras Theorem.

Pythagoras Theorem

`\rm a^2+b^2=c^2`

where:

• a and b are the legs of the right triangle.
• c is the hypotenuse (longest side) of the right triangle.

Given:

• a = height
• b = base = 6 ft
• c = hypotenuse = 15 ft

Substitute the given values into the formula and solve for a:

`\implies \rm a^2+6^2=15^2`

`\implies \rm a^2+36=225`

`\implies \rm a^2+36-36=225-36`

`\implies \rm a^2=189`

`\implies \rm √(a^2)=√(189)`

`\implies \rm a=√(9 \cdot 21)`

`\implies \rm a=√(9)√(21)`

`\implies \rm a=3√(21)`

`\implies \rm a \approx 13.75\:\:ft\:\:(nearest\:hundredth)`

Therefore, the height of the building is 13.75 ft (nearest hundredth).