SOLUTION: A boat is 92 feet from the base of a cliff. If the distance from the top of the cliff to the boat is 23 less than twice the height of the cliff to the water, find the height of th

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Question 446106: A boat is 92 feet from the base of a cliff. If the distance from the top of the cliff to the boat is 23 less than twice the height of the cliff to the water, find the height of the cliff. Round to the nearest tenth of afoot if necessary.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let height of cliff be x
distance from cliff to boat = 2x-3
distance from boat to cliff on ground = 92
Use Pythagoras theorem
(2x-3)^2=x^2+92^2
4x^2-12x+9=x^2+8464
3x^2-12x-8455=0
a= 3, b= -12, c= -8455

b^2-4ac=144+101460
b^2-4ac=101604
sqrt(101604)=318.75
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(12+318.75)/6
x1= 55.13
x2=(12-318.75)/6
x2=-51.13
Ignore negative value
Height = 55.13 ft
m.ananth@hotmail.ca