The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an angle of \[60{}^\circ \] with the horizontal, then the length of the wire is [SSC (CGL) 2013] |
A) \[8\sqrt{3}\,m\]
B) 8 m
C) \[6\sqrt{3}\,m\]
D) 6m
Correct Answer: A
Solution :
Let the length of the wire be \[l.\] |
In \[\Delta ADE,\] \[\sin 60{}^\circ =\frac{DE}{AD}\] |
[AD = length of wire] |
In \[\Delta ADE,\]\[\sin 60{}^\circ =\frac{DE}{AD}\] |
\[\Rightarrow \] \[\frac{\sqrt{3}}{2}=\frac{36-24}{l}\] |
\[\Rightarrow \] \[l=\frac{12}{\sqrt{3}}\times 2\] |
\[\therefore \] \[l=\frac{24}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=8\sqrt{3}\,m\] |
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