this a tan questien

Question

Shooter is on cliff on right side. Barrel height is 20. Target is on ground on left side, 500 to the left and 300 down. Target is .75 tall. What is angle of headshot (in radians)?

Answer 1

Hi Raynier, not sure if I have the picture correct: it sounds like the barrel is 20 feet high, on top of a 300-foot cliff, so the total distance from the ground is 320 feet. But the target is .75 foot high, so the vertical distance is 319.25 feet from the gun to the target.

So if you draw a triangle with the hypotenuse going from the target to the barrel and base along the ground, we have horizontal distance 500 and vertical distance 319.25. Then we'd probably want the cannon's angle down from the horizontal; this angle is the same as the target's angle looking up at the gun. So we'd have

tanθ = opp / adj = 319.25 / 500

Take tan^-1 of both sides:

θ = tan^-1(319.25 / 500) Make sure your calculator is set to "rad" not "deg." Answer should be somewhere around 0.57, kind of weird to use radians for this problem though.