Question

A boat is 104 feet from the base of cliff. If the distance from the top of the cliff to the boat is 26 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary. ​

Answer 1

Answer: h = 68.5, 51.2

Step-by-step explanation:

Draw a right angle triangle. The base is the sea and the line perpendicular to it is the cliff  

The base is the distance of from boat to the cliff is 104

Let the height of the cliff be h.

The hypotenuse, the distance from the top of the cliff to the boat is therefore 2h-26

Pythagoras tells us that  

(2h−26)^2  = 104^2 + h^2

4h^2 − 52h + 289 = 10816 + h^2

3h^2 − 52h − 10527 = 0

h=68.5, 51.2

The other result is negative and therefore not relevant.

If you cannot factorize then solve using the formula.