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The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =

a) 26
b) 16
c) 12
d) 10

Answer: c
Explanation: Let AB and CD are two poles AB = 10 m and CD = 16 m
q73
AC is wire which makes an angle of 30° with the horizontal
Let BD = x, then AE = x
CE = CD – ED = CD – AB = 16 – 10 = 6m
$$\eqalign{ & {\text{Now}}\,{\text{in}}\,\Delta ACE \cr & \sin {30^ \circ } = \frac{{CE}}{{AC}} = \frac{6}{l} \cr & \frac{1}{2} = \frac{6}{l} \cr & l = 2 \times 6 = 12\,m \cr} $$

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