10th Class
Mathematics
Introduction to Trigonometry
Question Bank
Trigonometry
question_answer
A man on the top of a bamboo pole observes that the angles of depression of the base and the top of another pole are \[60{}^\circ \] and \[30{}^\circ \] respectively. If the second pole stands 5 m above the ground level, then the height of the bamboo, on which the man is sitting, is
A) 5 m
B) 7.5 m
C) 10 m
D) 12.5 m
Correct Answer:
B
Solution :
From \[\Delta \,BMQ,\] \[x=y\,\cot \,{{30}^{o}}=\sqrt{3}y\] ??(i) From \[\Delta \,APQ,\] \[x=(y+5)\,\cot {{60}^{o}}\] or \[x=\frac{1}{\sqrt{3}}(y+5)\] ?..(ii) From equations (i) and (ii), we have \[\sqrt{3}y=\frac{(y+5)}{\sqrt{3}}\] or \[y=2.5\] \[\therefore \] Height of bamboo pole \[=PQ=PM+MQ\] \[=5+2.5\] \[=7.5\,m\]