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Angle of Depression

A tower HP st...

Question

A tower HP standing vertically at the orthocentre H of a triangle ABC subtends an angle A at the vertex A of the triangle. The height of the tower is....

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Solution

The distance of orthocentre H from the vertices A, B, C are $2 R c o s A, 2 R c o s B$ and $2 R c o s C$ where R is circum-radius of the triangle and $\frac{a}{s i n A} = 2 R$
$A H = H P c o t A$ or $2 R c o s A = h c o t A$
or $\frac{a}{s i n A} c o s A = h c o t A ∴ h = a$

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