SOLUTION: a security light is being installed outside a loading dock. the light must be placed at a 52 degree angle so that it illluminates a parking lot. if the distance from the end of t

Question 892765: a security light is being installed outside a loading dock. the light must be placed at a 52 degree angle so that it illluminates a parking lot. if the distance from the end of the parking lot to the loading dock is 100 feet, what is the height of the security light.?
am I using tangent to solve? not sure what to do.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
If the 52 degrees is between the wall and direction the light is pointing,
then the 100 feet is opposite from the 52 degree angle, and
the height of the light is the adjacent side of the triangle.
so tan(52) = opposite/adjacent = 100/adjacent
let x = the length of the adjacent side
tan(52) = 100/x
x*tan(52) = 100
divide each side by tan(52)
x = 100/tan(52)
x = 78.128 feet
If the 52 degrees is from horizontal, the angle of interest is 90-52 = 38 degrees
we would want to solve tan(38) = 100/x
and x = 100/tan(38) = 128 feet
In either case it seems unlikely we would expect to place a light that high.
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