A winch is used to tow a boat to a dock. The rope is attached to the boat at a point 15 feet below the level of the winch. Find the distance from the boat to the dock when there is 75 feet of rope out.

Question

I got 15^2+75^2=X^2. I put a square root around each side so I got 15+75=X^2, which is 90. I then put a square root sign around 90. Is this correct? I'm not sure if I should further reduce 90 into the square root of 9 and the square root of ten (3 times the square root of ten) or if I should just leave it be. How do you know when to reduce it and when not to (the example didn't try to reduce the sq. root). Thank you for your help.

Answer 1

It should be 75^2=15^2+x^2 or
x= sqrt (75^2-15^2)= sqrt5850=76.4 ft

I would use the calculator on something that asked for the distance. sqrt(75^2-15^2) is hardly what we mean by distance.

Answer 2

oops. I didn't use calculator.

sqrt(75^2-15^2)= sqrt(5400)=73.5 ft