question_answer

The angle of depression of two ships from the top of a light house are \[45{}^\circ \]and \[30{}^\circ \] towards East, If the ships are 200 m apart, the height of the light house is

A)  \[\frac{200}{\sqrt{3}-1}\,\,m\]

B)                     \[\frac{200}{\sqrt{3}+1}\,\,m\]

C)  \[\frac{100}{\sqrt{3}-1}\,\,m\]               

D)  \[\frac{100}{\sqrt{3}+1}\,\,m\]

Correct Answer: A

Solution :

Here, Applying shortcut method

Here, \[x=200\,\,\text{m},\]\[{{\theta }_{1}}=45{}^\circ ,\]\[{{\theta }_{2}}=30{}^\circ \]

\[h=\frac{x}{\cot {{\theta }_{2}}-\cot {{\theta }_{1}}}\]

\[=\frac{200}{\cot 30{}^\circ -\cot 45{}^\circ }\]

\[=\frac{200}{\sqrt{3}-1}\]

So, height of tower,

\[h=\frac{200}{\sqrt{3}-1}\text{m}\]