College Algebra help

Question

At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree.

Answer 1

If I could draw a right triangle I would put these unknowns as the sides of the triangles: h,, 35, and 1 + 3h. If you understand adjacent and opposite sides I will explain the picture of the triangle that way. The opposite side of the right angle or the Hypotenuse is 1 + 3h, the adjacent side of the right angle is 35  and the left side is 12

 

Solve for H.

 

h^2 + 35 ^2 = (1 + 3h) ^ 2

skipping steps you end up with

4h^2 + 3h - 612 = 0

(4h^2 + 51) (h - 12) = 0

 h = -12.75 or 12

 

The height can't be negative so the answer is 12.

 

If you check your answer 12 ^2 + 35 ^2 = ( 1 + 3(12))^2  TRUE.