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
:
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(6.83^2 + 3.83^2)}}}
h = 7.83 which is x+1