A force of 692 lb is required to pull a boat up a ramp inclined at 25 degree with the horizontal..

Question

How much does the boat weigh?

Answer 1

Draw the geometric diagram :

Based on the above figure, can make the following observations.

|| BA || = force of gravity = weight of the boat.

|| BC || = force against ramp.

|| AC || = force required to move boat up ramp = 692 lb.

By construction, triangle BWD and ABC are similar. Therefore, angle ABC is 25 degrees. So, in triangle ABC

sin 25^o = || AC || / || BA ||

sin 25^o = 692 / || BA ||

|| BA ||  = 692 / sin 25^o.

|| BA ||  ≅ 692 / (0.4226) ≅ 1637.4 lb.

The weight of boat is approximatelly 1637.4 lb.