A 15 ft ladder is leaning against a building. The base of the ladder is 5 ft from the building. How far up the building does the ladder go?

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Answer 1 · 2016-02-01T03:00:07

height#~~14.14ft#

Notice how this problem takes the shape of a triangle.

These are the following dimensions:

#1.# base#=5ft#
#2.# hypotenuse#=15ft#
#3.# height#=?ft#

To solve for the height, use the Pythagorean Theorem, which is:

#a^2+b^2=c^2#

where:
#a=#height
#b=#base
#c=#hypotenuse

Substitute your known values into the equation to find the height:

#a^2+b^2=c^2#

#a^2+(5)^2=(15)^2#

#a^2+25=225#

#a^2=200#

#a=sqrt(200)#

#a=10sqrt(2)rArr#simplify the radical

#a~~14.14ft#

#:.#, the ladder goes approximately #14.14ft# up the building.