question_answer

The angle of elevation of the top of a vertical tower from a point A, due east of it is \[{{45}^{o}}\]. The angle of elevation of the top of the same tower from a point B, due south of A is \[{{30}^{o}}\]. If the distance between A and B is \[54\sqrt{2}\]m, then the height of the tower (in metres), is   JEE Main Online Paper (Held On 10 April 2016)

A) 54                                              

B) 108

C) \[54\sqrt{3}\]                       

D) 36 3

Correct Answer: B

Solution :

                          \[\frac{{{\ell }^{2}}}{4}+{{(54{{v}_{2}})}^{2}}=\frac{3{{\ell }^{2}}}{4}\]         \[{{(54)}^{2}}\times 2\times 2={{\ell }^{2}}\] \[\ell =54\times 2=108\]