Find the function, graph, and a written explanation.
The fire chief has been drilling his crew in some new techniques with their hook-and-ladder truck, including maneuvers calling for the truck to approach a burning building very rapidly with the ladder extended to specific heights and at specific angles. Unfortunately the computer containing some of the critical data has crashed leaving only partial information. You would be wise to use and inverse sin function to model this data and help the chief continue his training program.
(For a specific angle, the length of the ladder is extended and the distance from the building to the base of the ladder are given as L and D respectively, while Y is the calculated y-value. All distances are given in feet.)
DATA TABLE:
(L): 105, 97, 102, 111, 105, 104, 112, 116, 103, 109, 98, 108, 114.
(D): 37, 52, 21, 35, 34, 37, 26, 32, 41, 38, 55, 63, 29.
(Y): -4.15, -6.47, -2.96, -3.69, -6.31, -6.01, -2.68, -3.20, -4.67, -5.76, -6.86, -7.12, -4.61.
So I played with the data and did some different plots.
If you plot the distance as the x axis and the angle in degrees on the y axis you get a pretty nice straight line. The closer you are to the building, the steeper the angle.
The formula I used was: y=cos^-1((D+Y)/L)*180/pi (my calculator was in radians)
I essentially used the y-values as a correction. And the function makes sense since if you're closer than 5.5 feet the angle is more than 90 degrees
Not sure why an inverse sine was recommended since you had the adjacent and the hypotenuse measures.