Emily is standing 150 feet from a circular target with a radius of 3 inches. To hit a bull's eye she msut hold the gunperfectly level. Will she hit the target if her aim is off by two-tenths of a degree in any direction?
2006-10-18 03:54:29 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
OK, let's model the situation. If the aim is off by 0.2 degrees, by how much will she miss the bullseye?
Draw a right triangle with a horizontal leg of 150, a vertical leg of x, and an angle of 0.2 degrees between the horizontal leg and the hypotenuse.
From trig, we know tan (0.2) = x/150
Therefore, x = 150*tan(0.2)
If you plug that into a calculator, you get x=0.52
Emily will miss the bullseye by 0.52 feet, or a bit over 6 inches. Since the target has a radius of 3 inches, she will miss the target.
2006-10-18 04:04:50 · answer #1 · answered by Bramblyspam 7 · 0⤊ 0⤋
Take the target radius, 3 in, divided by Emily's distance from the target, (150 ft)*(12 in/ft) = 1800 in, and find the arctangent of that number. That tells you the maximum angle Emily can deviate and still hit the target. If .2 degrees is greater that that maximum angle, then she misses. If it is less, then she hits the target. If you're not supposed to use arctangent, instead take the tangent of 0.2 degrees. If it's greater than the ratio you found above, she misses. If it's less, she hits.
2006-10-18 04:00:53 · answer #2 · answered by DavidK93 7 · 1⤊ 0⤋
No.
arctan(3/(12*150)) = 0.03183 < 0.2
2006-10-18 04:03:06 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋