Trigonometry but this makes no sense??

Question

The dock is 5 ft above the edge of a boat. If the boat is being pulled into the dock and has 32 ft of rope out, how far away from the dock is the boat?

Answer 1

It looks like you need to find the base of a right triangle whose height is 5 and hypotenuse is 32.  Try Pythagoras' theorem.

 

b = √(32² - 5²) ft ≅ 31.6 ft

 

You can also use trigonometry.

 

θ = angle between rope and water

 

sinθ = 5/32 = 0.15625

 

tanθ = sinθ/cosθ = 0.15625/√(1 - 0.15625²) ≅ 0.15819

 

b = h/tanθ = 5/0.15819 ft ≅ 31.6 ft