Question #b9110

1 Answer
smendyka
Jan 19, 2018

See a solution process below:

Explanation:

Because the ladder is at a #45^o# angle with the building the distance from the ground to the top of the ladder is the same as the distance from the base of the building to the bottom of the ladder.

We can then use the Pythagorean Theorem to find how far up the building the ladder goes.

Let's call the distance from the bottom of the building to the top of the ladder #s#.

The Pythagorean Theorem states:

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

Because both sides of the right triangle formed by the ground, and building are the same we can substitute #x# for #a# and for #b#

We are told the ladder, the hypotenuse in this problem is #14"ft"# so we can substitute this for #c#

#x^2 + x^2 = (14"ft")^2#

#2x^2 = 196"ft"^2#

#(2x^2)/color(red)(2) = (196"ft"^2)/color(red)(2)#

#x^2 = 98"ft"^2#

#sqrt(x^2) = sqrt(98"ft"^2)#

#x = sqrt(49 * 2)"ft"#

#x = sqrt(49)sqrt(2)"ft"#

#x = 7sqrt(2)"ft"#

The Answer Is: C #7sqrt(2)# feet

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