At a point on the ground 15 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. find the height of the tree.

The height and the distance from base (15 feet) are 2 legs of a right triangle.
The hypotenuse is distance from the point 15 ft from base to top of tree,
or 2(height) + 1ft.
.
Let a=height; b=distance from base=15 ft; c=hypotenuse=2a+1ft

a2 +b2=c2 (2 means square eg:a square +b square)

a2+(15ft)2=(2a + 1ft)2
a2+225ft2=4a2 +4a+1
0=3a+4a-224
0=(a-8)-(3a+28)
a-8=0 OR 3a +28=0
a=8 OR 3a=-28
a=8 OR a=28÷3

so a=8 ft

the height of the tree is 8ft