laser beam trig prob?

Question

A laser beam is to be directed through a small hole in the center of a circle of radius 10 ft. The origin of the beam is 35 ft form the circle. At what angle of elevation should the beam be aimed to ensure that it goes through the hole?

please help me and explain it to me, thanks guys!

Answer 1

We can infer from the statement of the problem that the circle is perpendicular to the horizon like a target, and the laser is being "fired" from ground level. The angle formed is part of a right triangle with opposite side of 10 feet and adjacent side of 35 feet. The tangent of that angle is then 10/35. We say :
tan A = 10/35 = 5/7
or:
A = arc tan(5/7)
The angle can be found with a scientific calculator using the inverse tangent or 2nd F tan function.
A = 15.945degrees

Here's the pic:

http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=laserangle10-18-07.jpg