SOLUTION: At a certain time of day a tree that is X meters tall cast a shadow that is X -3 m long if the distance from the top of the tree to the end of the shadow is X +1 m what is the heig

Algebra ->  Trigonometry-basics -> SOLUTION: At a certain time of day a tree that is X meters tall cast a shadow that is X -3 m long if the distance from the top of the tree to the end of the shadow is X +1 m what is the heig      Log On


   

Question 1148735: At a certain time of day a tree that is X meters tall cast a shadow that is X -3 m long if the distance from the top of the tree to the end of the shadow is X +1 m what is the height X of the tree
Found 3 solutions by ikleyn, ankor@dixie-net.com, William_KO:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

You have a right angled triangle with the legs  X and X-3  and the hypotenuse (X+1) meters.


    X%5E2 + %28X-3%29%5E2 = %28X%2B1%29%5E2

    X%5E2+%2B+X%5E2+-+6X+%2B+9 = X%5E2+%2B+2X+%2B+1

    X%5E2+-+8X+%2B+8 = 0


Use the quadratic formula


    X%5B1%2C2%5D = %288+%2B-+sqrt%288%5E2+-+4%2A8%29%29%2F2 = %288+%2B-+sqrt%2832%29%29%2F2 = %288+%2B-+4%2Asqrt%282%29%29%2F2 = 4+%2B-+2%2Asqrt%282%29


Only the root  X = 4+%2B+2%2Asqrt%282%29  makes sense.


ANSWER.  The height of the tree is  X=  4+%2B+2%2Asqrt%282%29 = 6.828 meters.

Solved.

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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At a certain time of day a tree that is X meters tall cast a shadow that is X -3 m long
if the distance from the top of the tree to the end of the shadow is X +1 m, what is the height X of the tree
:
This forms a right triangle: a^2 + b^2 = c^2; where
a = x
b = (x-3)
c = (x+1)
Using Pythagoras we have
x^2 + (x-3)^2 = (x+1)^2
FOIL
x^2 + x^2 - 6x + 9 = x^2 + 2x + 1
Combine like terms on the left
x^2 + x^2 - x^2 - 6x - 2x + 9 - 1 = 0
x^2 - 8x + 8 = 0
Use the quadratic formula a=1; b=-8; c=8
the two solutions
x = 1.17
and
x = 6.83, this is the only solution that makes sense (x-3)
therefore the tree is 6.83 m high
:
:
Check: find the hypotenuse using 6.83 and 3.83
h = sqrt%286.83%5E2+%2B+3.83%5E2%29
h = 7.83 which is x+1

Answer by William_KO(1) About Me  (Show Source):
You can put this solution on YOUR website!
(x+1)^2=(x-3)^2+x^2
(x^2+2x+1)=(x^2-6x+9)+x^2 square them
x^2+2x+1=2x^2-6x+9 move everything to the right side
0=x^2-8x+8 then use quadratic formula


x= 4+2 root 2 or 4-2 root 2
Hope this helps.