SOLUTION: Hello, I'm having a hard time solving this problem: A guy wire 40 feet long runs from the top of a pole to a spot on the ground. If the height of the pole is 5 feet more than the

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Question 913629: Hello, I'm having a hard time solving this problem:
A guy wire 40 feet long runs from the top of a pole to a spot on the ground. If the height of the pole is 5 feet more than the distance from the base of the pole to the spot where the guy wire is anchored, how tall is the pole?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
distance from base of pole leg1= x m
Height of pole leg2= x+ 5 m
wire , Hypotenuse = 40 m

Pythagoras theorem

(Hyp)^2= (leg1)^2+ Leg2^2
Hypotenuse = 40 cm
leg1= x cm
Leg2= (x + 5 )

x^2 + (x + 5 ) ^2 + = 1600
x^2 + x^2 + 10 x+ 25 = 1600
2 x^2+10x -1575 = 0
/ 2
1 X^2 + 5 x-787.5 = 0
Find the roots of the equation by quadratic formula

a= 1 ,b= 5 ,c= -787.5

b^2-4ac= 25 - -3150
b^2-4ac= 3175
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%2812%29
x1=( 51.35)/ 2
x1= 25.67 ft
x2=( -5 -56.35 ) / 2
x2= -30.67
Ignore negative value
Height of pole = 25.67+5= 30.67m