From the top of a house, $^{'} h^{'}$ meters high from the ground, the elevation and depression of the top and bottom of a tower on the other side of the street are $θ$ and $ϕ$ respectively. Prove that the height of the tower is $h (1 + tan θ cot ϕ)$

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Solution

$t a n θ = (\frac{l - h}{d}) \to (1) a n d t a n ϕ = (\frac{h}{d}) \to (2) d i v i d e (1) b y (2) t a n θ c o t ϕ = (\frac{l - h}{h}) o r h t a n θ c o t ϕ = l - h h (1 + t a n θ c o t ϕ) = l$

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