Problema Solution
At a certain time of day, a tree that is x feet 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, what is the height, x, of the tree?
Answer provided by our tutors
we will consider the tree to be perpendicular to its shadow.
thus we have a right triangle with legs x and x - 35 and hypotenuse equal to x + 5. Using the Pythagorean Theorem we have
x^2 + (x - 35)^2 = (x + 5)^2
x^2 + x^2 - 70x + 1225 = x^2 + 10x + 25
3x^2 - 80x + 1200 = 0
by solving the quadratic equation we find 2 solutions
x1 = 60 meters
x2 = 20 meters this is not a solution since x - 35 = 20 - 35 = -15 < 0 the length of the shadow
the heights of the tree can be 60 meters.