boat is pulled into dock with rope attached to boat at water level when boat is 12ft from dock, length of rope from boat to dock is 3 ft longer than twice height of dock above water. find height dock

Question

need help solving this problem from a worksheet. the answer has to be in a complete sentence with the correct units

Answer 1

The hypotenuse of the triangle is the rope. It is 3+2h

use Pythagorean theorem a= distance from boat to the dock is 12. so find the height of the dock

c²=a² +b²

(3+2h)²= 12²+ h²

9+4h²+12h=144+h²

3h²+12h-135=0

h²+4h-45=0

(h+9)(h-5)=0

h= -9 or h=5

since the height cannot be below the water, so the height is 5.

Answer 2

Hi Bridget the Math Person,

The way I read this is that 3 more than twice something (the height of the dock) is 12.

So, the suggested equation is 2h + 3 = 12.

I think you can take it from there!