A spherical balloon of radius 15 feet subtends an angle 60∘ at the eye of an observer. If the angle of elevation of its center is 45∘, find the height of the center of the balloon.
Answer:
15√2 feet
- The following picture shows the observer at point A, observing a balloon.
- Let's assume the height of the center of the balloon to be h, therefore OB=h
Also, assume the distance of center of the balloon from observer to be D, therefore OA=D - For triangle △OAP,
- For
- On equating two values of from equation and