A boat is 300 feet from the base of a cliff If the distance

A boat is 300 feet from the base of a cliff. If the distance from the top of the cliff is 75 more than twice the height of the cliff. Find the height of the cliff.

Solution

distance between boat and base of the cliff = 300 ft

Assuming height of cliff = h

distance between boat and top of the cliff = 2h + 75

Now using pythagoras theoram:

h^2 + 300^2 = (2h + 75)^2

h^2 + 90000 = 4h^2 + 300h + 5625

3h^2 + 300h - 84375 = 0

h^2 + 100h - 28125 = 0

Solving above equation:

h = 125 feet

height of the cliff = 125 ft