Adam needs a supporting beam. the dam leans at an 80 degree angle and is 200 ft tall. if the base of the supporting beam is placed 75 feet from the base of the dam and the beam extends to the top of the dam, how long must the beam be?

If we set this up as a right triangle, the height of the dam is the hypotenuse, the base is 75, the distance from the base of the dam to where the beam will be, and and we are looking for the height of the beam, which happens to be across from the reference angle we are given of 80.  We could solve this in a couple of different ways, but I will use the sin ratio, which is and 200 sin80 = x.  Using our calculator, we find that x = 196.96.  I guess this all depends upon your angle.  Is the 80 degrees made with the ground? If so, then this is the correct answer.  If the angle is made with its upright position of 90, then it would be 10 degrees from the ground. 

Check the picture below.

make sure your calculator is in Degree mode.

Top right since it passes vertical line test