EXAMPLE 5 A man walks along a straight path at a speed of6fts. A searchlight is located on the ground 10ft from the path and is kept focused on the man.At what rate is the searchlight rotating when the man is24ft from the point on the path closest to the searchlight?SOLUTION We draw the figure to the left and let xbe the distance from the man to the point on the path closest to the searchlight. We let be the anglebetween the beam of the searchlight and the perpendicular to the path.We are given that dxdt=6fts and are asked to find ddt when x=24. The equation that relates x and canbe written from the figure:x,-=tan(),x=10,tan()Differentiating each side with respect tot,we getdxdt=10(sec2()),ddtsoddt=110sec2(),dxdt=(110sec2())=0.0887574When x=24, the length of the beam is26,socos()=1026 andThe searchlight is rotating at a rate of,rads.please get this correct, the problems with a red x are incorrect and ive tried like everything, the answer is not 0.0888