The angle of depression of a boat A from the to... - SS2 Mathematics Trigonometric Ratios II Question
The angle of depression of a boat \(A\) from the top of a cliff \(21m\) high is \(42{^\circ}\). The angle of depression of another boat \(B\) in the straight line as \(A\) and from the same point is \(25{^\circ}\). Find the distance between the two boats.
\(distance\ bewteen\ boats\ A\ and\ B = distance\ of\ B\ from\ cliff - disatnce\ of\ A\ from\ cliff\)
\[disatnce\ of\ A\ from\ cliff:\]
\[\tan{42{^\circ}} = \frac{21}{OA}\]
\[OA = \frac{21}{\tan{42{^\circ}}} = \frac{21}{0.9004} = 23.32m\]
\[disatnce\ of\ B\ from\ cliff:\]
\[\tan{25{^\circ}} = \frac{21}{OB}\]
\[OB = \frac{21}{\tan{25{^\circ}}} = \frac{21}{0.4663} = 45.04m\]
\[distance\ bewteen\ boats\ A\ and\ B = distance\ of\ B\ from\ cliff - disatnce\ of\ A\ from\ cliff\]
\[distance\ bewteen\ boats\ A\ and\ B = 45.04 - 23.32 = \ 21.72m\]
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