Alex O.

asked • 05/21/17

"A long range marksmen wants to compute the distance to a target...

He places the the cross-hair of his scope on the bottom of target and reads the angle between the top and bottom of the target as 3.5 milliradians (1 milliradian=1/1000 radians). If the target is 1.5 meters tall, find the distance to the target. Round to the nearest meter." Hello, I am sure I need to enter the data as sides of a triangle, then use the trigonometric functions and such to find the sides. But, I keep getting the wrong answers, and to be honest, I am not sure I am even doing it correctly. Can someone help?

Kenneth S.

I'm not interested in guns, but I will note that the title should be A marksman...(because marksmen is plural).
 
Be sure to convert your angles to degrees, and put your calculator into Degree mode.
 
Is your depiction of this situation a right triangle with vertical leg1.5 m, the distance d from marksman's rifle to target being the horizontal leg and the angle of elevation θ = 0.0035 radians?  This can be solved easily by tan θ 1.5/d. But the problem is, that assumes that the rifle is at ground level (therefore the triangle is a right triangle).
 
 
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05/21/17

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Arturo O. answered • 05/21/17

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y = height of target
x = horizontal distance to target
θ = the measured angle
 
tanθ = y/x
 
x = y / tanθ
 
The measured θ is in milliradians.  Did you set your calculator in the radian mode?
 
θ = 3.5 x 10-3 rad
 
x = (1.5 m) / tan(3.5 x 10-3) ≅ 429 m
 
 
 
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