Question

A building with ten storeys, each storey of height 3 metres, stands
on one side of a wide street. From a point on the other side of the
street directly opposite to the building, it is observed that the three
uppermost storeys together subtend an angle equal to that subtended
by the two lowest storeys. What is the width of the street ??

Answer 1

choose 3 angles , A,B,C such that A-B =C
\[\tan A = \frac{30}{x}\]
\[\tan B = \frac{21}{x}\]
\[\tan C = \frac{6}{x}\]
\[\rightarrow \tan (A-B) = \tan C\]
\[\rightarrow \frac{\tan A -\tan B}{1+\tan A \tan B} = \tan C\]
substitute in ratios and solve for x
x = 35.5