question_answer

A tree is broken by wind, its upper part touches the ground at a point 10 m from the foot of the tree and makes an angle of\[45{}^\circ \]with the ground. The total length of tree is

A)  \[10(1+\sqrt{2})m\]

B)  \[10\left( 1+\frac{\sqrt{3}}{2} \right)m\]

C)  15 m             

D)  20 m

Correct Answer: A

Solution :

 Let AB is a tree of height n and\[QC=BC\] In \[\Delta ADC,\cos 45{}^\circ =\frac{DA}{DC}\] \[\Rightarrow \] \[\frac{1}{\sqrt{2}}=\frac{10}{DC}\] \[\Rightarrow \] \[DC=10\sqrt{2}\] and \[AC=DC\sin 45{}^\circ =10\sqrt{2}.\frac{1}{\sqrt{2}}=10\] Hence, height of the tree, \[n=AC+DC\] \[=10+10\sqrt{2}\] \[=10(1+\sqrt{2})m\]