SOLUTION: At a certain time of day, a tree that is x meters tall casts a shadow that is x-35 meters long if the distance from the top of the tree to the end of the shadow is x+5 meters long,

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Question 981751: At a certain time of day, a tree that is x meters tall casts a shadow that is x-35 meters long if the distance from the top of the tree to the end of the shadow is x+5 meters long, what is the height, x, of the tree
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Consider the tree and its shadow
as a right angled triangle
The tree = 'x'
The shadow = x - 35
The distance from the top of the
tree to the end of the shadow
= x + 5
Using Pythagoras:
x^2 + (x - 35)^2 = (x + 5)^2
x^2 + x^2 - 70x + 1225 = x^2 + 10x + 25
Collect like terms
x^2 + x^2 - x^2 -70x - 10x + 1225 - 25 = 0
x^2 - 80x + 1200 = 0
Factorise
(x - 20)(x - 60) = 0
x - 20 = 0
x = 20 (No answer as side x - 35 would give a negative answer)
x - 60 = 0
x = 60
This is the height of the tree = 60 metres
Hope htis helps:-)