need to calculate the angle of impact of some stains and than use the tan equation to get the height of origin in inches

Question

Stain 1: width of stain is 7.2 mm, the length is 14.4 mm what is the degree of impact. I have tried converting to fractions or decimals and I still do not get it. I need step by step instructions.

 

Then I need to use the tan equation to figure out the height of origin in inches. I know the distance from point of convergence which is 37.5 inches how do I get the height of origin in inches.  HELP!

 

How did you find the arccsc that equaled 30 degrees

Answer 1

If you visualize the path of the droplet, it's really a cylinder that is cut by the surface on which the stain hits.  The width of the stain would always be the diameter of the droplet, but the length would depend on the angle of impact.

 

If the stain hits from straight above (90°), the stain would be a circle, so the ratio of the length to the width would be 1.  If the stain hits from an almost horizontal angle (0°), the length would be much larger than the width.  If you think about it, the ratio of the length to the width is going to be the cosecant of the angle of impact.

 

So the ratio in this case is 14.4 / 7.2 = 2.  Find the arccsc of 2 -- that's 30°.

 

I'm not sure exactly what "distance from point of convergence" means, but since they want you to use the tan function to find the height, I'd conclude that it means the HORIZONTAL distance from the stain to the origin.

 

So the height and the distance from point of convergence form two legs of a right triangle.  (Height) / (distance from point of convergence) = tan (angle of impact).  In other words,

 

H / 37.5 = tan 30° = √3 / 3 = 0.577

 

So H = 37.5 * 0.577 = 21.638 inches