10th Class
Mathematics
Introduction to Trigonometry
Question Bank
Trigonometry
question_answer
The angles of elevation of the top of a tower from two points distant a and b (a > b) from its foot and in the same straight line from it are \[30{}^\circ \] and \[60{}^\circ \]. The height of the tower is
A)
\[\frac{a}{b}\]
B)
\[\sqrt{\frac{a}{b}}\]
C)
\[ab\]
D)
\[\sqrt{ab}\]
Correct Answer:
D
Solution :
From \[\Delta \,\,AOT,\] \[h=a\,\,\tan \,{{30}^{o}}\] From \[\Delta \,BOT,\] \[h=b\,\tan {{60}^{o}}\] \[\therefore \] \[{{h}^{2}}=ab\,\,\tan {{30}^{o}}\tan {{60}^{o}}\] \[=ab\,\frac{1}{\sqrt{3}}.\sqrt{3}\] or \[h=\sqrt{ab}\]