A museum has a security system to guard its valuable artifacts. The system is a beam that is situated (on the floor) on one side of a 40-ft. hallway and spreads outward at a 12-degree angle. It has been adjusted by museum officials so that the top of the beam ends up at the top of the opposite wall, which is 10 feet high. No criminal can go over the beam but it would be possible to pass undetected underneath the beam.
A villainous trigonometry student has decided to rob the museum and has gathered (he thinks) enough knowledge to break in. He can fit himself through a rectangle, when sliding along the floor, with width of 2 feet and height 16 inches. He thinks he will make it safely under the security beam if he crosses underneath as closely as possible to the opposite wall.
1.) Will he make it under the beam?
2.) By how much will he make or miss by?
3.) What should the smallest angle of light be so the museum hallway is safely guarded?
A villainous trigonometry student has decided to rob the museum and has gathered (he thinks) enough knowledge to break in. He can fit himself through a rectangle, when sliding along the floor, with width of 2 feet and height 16 inches. He thinks he will make it safely under the security beam if he crosses underneath as closely as possible to the opposite wall.
1.) Will he make it under the beam?
2.) By how much will he make or miss by?
3.) What should the smallest angle of light be so the museum hallway is safely guarded?
