SOLUTION: The base of a 20 foot ladder is 15 feet from a house. How far up the house does the ladder go? I asked this question already but the answer was not worked with the quadratic formu

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Question 524816: The base of a 20 foot ladder is 15 feet from a house. How far up the house does the ladder go? I asked this question already but the answer was not worked with the quadratic formula and i need to know how to solve in quadratic formula
Found 2 solutions by solver91311, Maths68:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Using the quadratic formula on this problem is a lot like killing a housefly with a 12 gauge shotgun, but we aim to please...

Presuming that the ground in the area of the bottom of the house wall and the bottom of the ladder is perfectly perpendicular to the wall of the house (mostly because unless this is true you cannot solve the problem with the information given), use Pythagoras. Let represent the distance from the ground to the top of the ladder measured along the wall.







Put it into standard quadratic form:



So

, , and

Then



Do the arithmetic and discard the negative root since distance is a positive number.

John

My calculator said it, I believe it, that settles it
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Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!


Given
Hypotenuse= 20feet
Perpendicular = Height
Base=15feet

Use Pythagoras' Theorem
(Hypotenuse)^2=(Perpendicular)^2+(Base)^2
(20)^2=(Height)^2+(15)^2
400=(Height)^2+225
400-255=(Height)^2
175=(Height)^2
(Height)^2 = 175
Take square root
sqrt(Height)^2 = sqrt(175)
Height=13.228
Height=13.23 feet