Problema Solution
at a point on the ground 70 ft from the base of a tree, the distance to the top of the tree is 2 ft more than 3 times the height of the tree. find the height of the tree
Answer provided by our tutors
let
b = 70 ft the distance to the base
a = the height of the tree, a>0
c = the distance to the top of the tree, c>0
the distance to the top of the tree is 2 ft more than 3 times the height of the tree
c = 2 + 3a
by using the Pythagorean theorem we have
c^2 - a^2 = b^2
plug c = 2 + 3a and b = 70 into the last equation
(2 + 3a)^2 - a^2 = 70^2
by solving we find
a = 24 ft
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the height of the tree is 24 feet.