question_answer

A boat man can row with a speed of 10 km/h in still water. If the river flows at 5 km/h, the direction in which the boat man should row to reach a point on the other bank directly opposite to the point from where he started is (width of the river is 2 km):

A)  in a direction inclined at\[120{}^\circ \]to the direction of river flow

B)  in a direction inclined at\[90{}^\circ \]to the direction of river flow

C) \[60{}^\circ \]in the north-west direction

D)  should row directly along the river flow

E)  none of the above

Correct Answer: A

Solution :

\[\sin \theta =\frac{CB}{AC}=\frac{5}{10}=\frac{1}{2}\Rightarrow \theta =30{}^\circ \] \[\therefore \]\[\theta =180{}^\circ -\angle ACB\]                 \[=180{}^\circ -[180{}^\circ -(90{}^\circ +30{}^\circ )]\]                 \[=180{}^\circ -60{}^\circ =120{}^\circ \]