# A boat is 68 feet from the base of cliff. If the distance from the top of the cliff to the boat is 17 less than twice the height of the cliff to the water. How do you find the height of the cliff?

Dec 3, 2016

51

#### Explanation:

Draw a right angle triangle . The the base is the sea and the line perpendicular to it is the cliff
The base , i.e. distance of from boat to the cliff is 68
Let the height of the cliff be h.
The hypotenuse, the distance from the top of the cliff to the boat is therefore 2h-17
Pythagoras tells us that ${\left(2 h - 17\right)}^{2} = {68}^{2} + {h}^{2}$
$4 {h}^{2} - 68 h + 289 = 4624 + {h}^{2}$
$3 {h}^{2} - 68 h - 4335 = 0$
Factorise
$\left(3 h + 85\right) \left(h - 51\right)$
h=51
The other result is negative and therefore not relevant .
If you cannot factorise then solve using the formula.