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The lower 24m portion of a 50m tall tower is painted red and rest is painted green. What is the distance of a point on the ground where the two different portions of the tower subtend equal angles

Answer 1

120 m is the distance of a point on the ground where the two different portions of the tower subtend equal angles

Step-by-step explanation:

Let say Angle subtended by Each portion = α

Then Angle subtended by Whole Tower = 2α

Tan2α  =  50/d

Tanα  = 24/d

=> 50/Tan2α  = 24/Tanα

=> Tan2α    = 50Tanα/24

=>  Tan2α    = 25Tanα/12

= 2Tanα/(1 - Tan²α)  =  25Tanα/12

=> 24/(1 - Tan²α)  =  = 25

=> 24 = 25 - 25Tan²α

=> 25Tan²α = 1

=> Tan²α = 1/25

=> Tanα = 1/5

Tanα  = 24/d

=> 1/5  = 24/d

=> d = 24 * 5

=> d = 120

120 m is the distance of a point on the ground where the two different portions of the tower subtend equal angles

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