question_answer

A vertical tower PQ subtends the same angle of \[30{}^\circ \] at each of the two places A and B 60 m apart on the ground. If AB subtends an angle of \[120{}^\circ \] at P, the foot of the tower. The height of the tower is -

A) 10 m                

B)        20 m

C) 30 m                

D)        40 m

Correct Answer: B

Solution :

[b] Let PQ=h and PB=x=PA then tan \[30{}^\circ =\frac{h}{x}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x}\] \[\Rightarrow x=\sqrt{3}h\] using sine rule in APAB \[\frac{PA}{\sin 30{}^\circ }=\frac{AB}{\sin 120{}^\circ }\] \[\Rightarrow x=\frac{60.\sin 30{}^\circ }{\sin 120{}^\circ }\] \[\Rightarrow \sqrt{3}h=60\times \frac{1}{2}\times \frac{2}{\sqrt{3}}\] \[\Rightarrow \]   \[h=20\,m\]