Question

The angle of depression of the top and bottom of a 12m tall building from the top of a multi storeyed building are 30 and 60 respectively find the height of the multistoried building

Answer 1

Given :- (from image) .

• AB = Building = 12m = DC.
• EC = multi storeyed building = Let H m.
• ∠EAD = 30° .
• ∠EBC = 60° .

Solution :-

in Right ∆EAD, we have ,

→ Tan 30° = ED / AD

→ (1/√3) = ED / AD

→ AD = √3ED ------------ Eqn.(1)

Similarly, in Right ∆EBC, we have,

→ BC = AD

→ EC = ED + DC

→ H = (ED + 12) { AB = DC. }

→ BC = AD

So,

→ Tan 60° = H/BC

→ √3 = H/BC

→ H = √3BC

→ H = √3AD

→ ED + 12 = √3AD

Putting value of Eqn.(1) ,

→ ED + 12 = √3(√3ED)

→ ED + 12 = 3ED

→ 3ED - ED = 12

→ 2ED = 12

→ ED = 6 m.

Therefore,

→ H = ED + 12

→ H = 6 + 12

→ H = 18 m. (Ans.)

Hence, the height of the multistoried building is 18m.

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Answer 2

Answer:

hope this helps u!!.......

answer = 18m