Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag
staff of height h. At a point on the plane, the angles of elevation of the bottom and
the top of the flag staff are alpha and bita, respectively. Prove that the height of the tower is (htana/tanb-tana)
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Answer 1

answer

Let height be y Δ OAC

tan θ= B÷P

tan β= OA÷CA

tan β= x÷y+h (y+h)→ Let AB, AB+BC

Let OA→ x

x=[tan β÷y+x]

Consider Δ OAB

tan α= x÷y

= Base÷perpendicular

x= tan α÷y

tan α÷y = tan β÷y+h

y tan β=tan αy+tanαh

y tan β−tany=tanαh

y(tanβ−tanα)=tanαh÷y= tanβ−tanα÷htanα

This