A rectangular swimming pool is 15ft by 40ft A rope is drawn diagonally across the top of pool Determine the sine & cosine of angle the rope makes with the longer side

Expert Answers
sciencesolve eNotes educator| Certified Educator

You should notice that a right angle triangle is formed by the rope with the sides of swimming pool.

The rope represents the hypotenuse of the right angle triangle and you should determine the sine and cosine of the angle made by hypotenuse to 40 ft leg of triangle such that:

`sin alpha = 15/h`

`cos alpha = 40/h`

You should use Pythagorean theorem to find the hypotenuse such that:

`h^2 = 15^2 + 40^2`

`h^2 = 225 + 1600`

`h = sqrt1825 =gt h = 5sqrt73`

You should substitute `5sqrt73 ` for h such that:

`sin alpha = 15/(5sqrt73) =gt sin alpha = 3/sqrt73`

`sin alpha = 3sqrt73/73`

`cos alpha = 40/(5sqrt73) =gt cos alpha = 8sqrt73/73`

Hence, evaluating the sine and cosine of the angle that hypotenuse makes to the longer side yields sin `alpha = 3sqrt73/73 ` and `cos alpha = 8sqrt73/73` .