A) \[50\,m\]
B) \[25\,m\]
C) \[40\,m\]
D) None of these
Correct Answer: B
Solution :
DP is a clock tower standing at the middle point D of BC. |
\[\angle PAD=\alpha ={{\cot }^{-1}}3.2\Rightarrow \cot \,\alpha =3.2\] |
and \[\angle PBD=\beta ={{\operatorname{cosec}}^{-1}}2.6\Rightarrow \operatorname{cosec}\,\beta =2.4\] |
\[\therefore \,\,\cot \beta =\sqrt{\left( \cos e{{c}^{2}}\beta -1 \right)}=\sqrt{\left( 5.76 \right)}=2.4\] |
In the triangles PAD and PAD, |
\[AD=h\cot \alpha =3.2h\] and \[BD=h\,\cot \beta =2.4\,h\] |
In the right angled \[\Delta ABD,A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\] |
\[\Rightarrow \,\,{{100}^{2}}=[{{(3.2)}^{2}}+{{(2.4)}^{2}}]{{h}^{2}}=16{{h}^{2}}\Rightarrow h=25m.\] |
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