question_answer

The angle of elevation of the top a tower from two places situated at distances 21m. And x m. from the base of the tower are \[45{}^\circ \] and \[60{}^\circ \] respectively. What is the value of x?

A) \[7\sqrt{3}\]

B) \[7-\sqrt{3}\]

C) \[7+\sqrt{3}\]

D) 14

Correct Answer: A

Solution :

[a] In \[\Delta ADB,\,\,\,\tan 45{}^\circ =\frac{AD}{BD}=\frac{AD}{21}\] \[AD=21\,m\] In \[\Delta ADC,\,\,\,\tan \,60{}^\circ =\frac{AD}{x}\] \[x=\frac{21}{\sqrt{3}}=7\sqrt{3}\,m\]