a flag on a top of a pole cast a shadow over a nearby hemispherical done with the tip of the shadow falling 10m away from the dome .if the base of the pole was 20m away from the diametric opposite end of the dome and the height of the pole was 50 m ,what would be the height. of the dome?
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Height of Dome = 20 m
Step-by-step explanation:
Let say Dome height = 2h
Then Diameter of Sphere = 2h
Radius of Sphere = 2h/2 = h
50/(20 + 2h + 10) = 2h/(10 + h)
=> 500 + 50h = 2h(30 + 2h)
=> 500 + 50h = 60h + 4h²
=> 4h² + 10h - 500 = 0
=> 2h² + 5h - 250 = 0
=> 2h² + 25h - 20h - 250 = 0
=> h(2h + 25) - 10(2h + 25) = 0
=> (h - 10)(2h + 25) = 0
=> h = 10
2h = 20
Height of Dome = 20 m
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