A spherical balloon of radius 1515 feet subtends an angle 6060 at the eye of an observer. If the angle of elevation of its center is 45,45, find the height of the center of the balloon.


Answer:

152 feet 152 feet 

Step by Step Explanation:
  1. The following picture shows the observer at point A,A, observing a balloon.
  2. Let's assume the height of the center of the balloon to be h,h, therefore OB=hOB=h
    Also, assume the distance of center of the balloon from observer to be D,D, therefore OA=DOA=D
  3. For triangle OAP,OAP,
    sinOAP=RDsin602=RDsin30=RD12=RDD=2R(1)
  4. For AOB,
    sinOAB=hDsin45=hD12=hDD=2h(2)
  5. On equating two values of D from equation (1) and (2),
    2h=2Rh=R2h=152 feet 

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