Find the area of the shaded region in the figure For the am

Find the area of the shaded region in the figure. () For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel Is 200 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time In seconds. Let theta be the angle between the line of your horizon and your line of sight to the elevator. Find a formula for h(t), the elevator\'s height above the ground as it descends from the top of the hotel. Using your answer to part (a), express theta as a function of time t.

Solution

Area of sector=(n/360)( pi*r²⁾

n is the sector angle which is pi/3 here

          =(pi/3/360)( 3.14*12²)=75.36

Area of triangle= multiplication of the two sides and sine of the including angle divided by2

                      =(12)(12)sin(pi/3)/2=62.35

Area of unshaded part= area of circlsector -area of triangle= 75.36-62.35=13.01

Area of shaded part= area of circle-area of unshaded part= (pi*12²- 13.01)= 439.15=439.2