Question

A window of a house is 2 m above the ground . From the window ,the angles of elevation

and depression of the top and bottom of another house situated on the opposite side of the lane

are found to be 60 o and 45o

respectively. Find the height of the house.
pls give step by step explanation​

Answer 1

Given :- (from image)

• AB = 2m . (window above the ground.)
• EC = another house.
• ∠EAD = 60° .
• ∠ACB = 45° .
• ED = let h .

Solution :-

in Right ∆ABC , we have,

→ Tan 45° = AB / BC

→ 1 = 2/ BC

→ BC = 2m.

in Right ∆ADE, we have

→ ED = h .

→ AD = BC = 2m.

so,

→ Tan 60° = ED / AD

→ √3 = h / 2

→ h = 2√3 .

Therefore,

→ EC = ED + DC

→ EC = h + AB . (∵ DC = AB.)

→ EC = 2√3 + 2

→ EC = 2(√3 + 1)

→ EC = 2(1.732 + 1)

→ EC = 2 * 2.732

→ EC = 5.464 m . (Ans.)

Hence, the height of the house is 5.464 m.

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