At a point on the ground 60 ft from the base of a tree, the distance to the to top of the tree is 4 ft more than 2 times the height of the tree. Find the height of the tree

Answer 1

Right triangle

one leg is T = height of tree

other leg is 60

hypotenuse is 4 + 2T

Pythagorean says:

T^2 + 60^2 = (4+2T)^2

T^2 + 3600 = 16 + 16T + 4t^2

0 = 3t^2 + 16t - 3584

0 = (3t + 112 )(t - 32 )

3t+112=0 results in negative measures and is disqualified

t-32 = 0 --> t = 32

height of the tree is 32....

CHECK

32^2 + 60^2 = 4624 = 68^2 = (2*32+4)^2

Yes, the tree is 32 feet tall