question_answer

The angle of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are \[43{}^\circ \] and \[47{}^\circ \] respectively. What is the height of the tower?

A) 40 m

B) 42 m

C) 45 m    

D) 47 m

Correct Answer: B

Solution :

[b] \[AB=h\] (height of the tower)

\[BD=36m;\]      \[BC=49m\]

\[\angle D=47{}^\circ ;\]            \[\angle C=43{}^\circ \]

Now, in \[\Delta ABD,\]

\[\tan 47{}^\circ =\frac{h}{36m}\]                                             ? (i)

and in \[\Delta ABC,\] \[\tan 43{}^\circ =\frac{h}{49m}\]

\[\tan (90{}^\circ -47{}^\circ )=\frac{h}{49}\]

\[\therefore \cot 47{}^\circ =\frac{h}{49}\]                      (ii)

Multiplying equations (i) and (ii)

\[\tan 47{}^\circ .\cot 47{}^\circ =\frac{h}{36}\times \frac{h}{49}=1=\frac{{{h}^{2}}}{36\times 49}\]

\[h=6\times 7=42m\]

\[\therefore \] Option [b] is correct