question_answer

The angle of depression of a boat m in a river is \[{{30}^{o}}\] from the top of a tower, \[87\text{ }m\]high and the speed of the boat is\[5.8\text{ }km/h\]. The time taken by the boat to reach at the base of the tower is

A)  \[9\,\,\min \]

B)  \[\frac{9\sqrt{3}}{10}\,\,\min \]

C)  \[25\,\,\min \]

D)  \[15\,\,\min \]

Correct Answer: B

Solution :

In \[\Delta \,ABC,\] \[\tan \,{{30}^{o}}=\frac{87}{x}\] \[\Rightarrow \] \[x=87\times \sqrt{3}m\] \[\therefore \] \[Speed=\frac{\text{distance}}{time}\] Time \[=\frac{87\times \sqrt{3}\times 60}{5.8\times 1000}=\frac{9\sqrt{3}}{10}\,\min \]