The angles of depression of the top and bottom of a 50 m high electric pole form the top of a building are 30anddeg; and 60anddeg; respectively. Find the height of the building.a)60 mb)70 mc)75 md)80 mCorrect answer is option 'C'. Can you explain this answer?

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The angles of depression of the top and bottom of a 50 m high electric pole form the top of a building are 30° and 60° respectively. Find the height of the building.

a)
60 m
b)
70 m
c)
75 m
d)
80 m

Correct answer is option 'C'. Can you explain this answer?

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The angles of depression of the top and bottom of a 50 m high electric...

According to the figure,
DE is the electric pole (height = 50m), AB is the building.
∠ADC = 30° & ∠AEB = 60°
We have to find out the length of AB.
As, DC ⊥ AB & EB ⊥ AB so, DC || EB
⇒ DE = BC
Also, DE || AB so, DC = EB
Now, AD × cos30° = DC & AE × cos 60° = BE
⇒ AD × cos30° = AE × cos 60°
⇒ √3 ×AD = AE
From the figure, AB = AC + BC
⇒ AB = AC + DE [As, DE = BC]
⇒ AE × sin 60° = AD × sin 30° + 50
⇒ √3 ×AD × sin 60° = AD × sin 30° + 50
⇒ AD = 50
Now, AB = AD × sin 30° + 50
⇒ AB = 25 + 50 = 75 meter.
The height of the building = 75 meter

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The angles of depression of the top and bottom of a 50 m high electric pole form the top of a building are 30° and 60° respectively. Find the height of the building.a)60 mb)70 mc)75 md)80 mCorrect answer is option 'C'. Can you explain this answer?

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