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MacGyver's escape (Trig Help!)?
MacGyver is on a mission to get out of a locked room. The entrance is guarded by a guard who is pacing away from the entrance and back. MacGyver looks through a crack and uses one of his contraptions to determine that the guard is walking at a rate of 3 feet per second. He pulls out the protractor and straw that he keeps in his pocket and places them is the crack. He can then measure the angle of depression from his location to the farthest point on the ground of the guard's path to be 7 degrees. He then uses another object that is lying around to measure the crack to be 5 feet above the ground. He uses all this information to determine how much time he has to escape after he gets the entrance opened.
How long does MacGyver have to escape (how long is the guard's back facing him)?
2 Answers
- SueLv 79 years agoFavourite answer
Angle of depression is equal to angle of elevation.
Let x= the farthest distance the guard is away from the crack.
tan 7 = 5/x
x= 5 /tan 7
x= 40.7 feet
40.7 ft / 3 f/s
13.5666 sec
- ?Lv 69 years ago
The distance the guard's back is away from the entrance to MacGyver's locked room is 5/tan(7degrees) feet
divide that distance by the guard's walking rate = [5tan(7)]/3 ft/sec = 10 seconds {there can only be one significant digit in the answer since there is only one significant digit in "5 feet"
