Question
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is
Answer: Option A
Let AB and CD be two poles
AB = 20 m, CD = 14 m
A and C are joined by a wire
CE || DB and angle of elevation of A is 30°
Let CE = DB = x and AC = L
Now AE = AB - EB = AB - CD = 20 - 14 = 6 m
$$\eqalign{
& {\text{Now in right }}\Delta ACE, \cr
& \sin \theta = \frac{{{\text{Perpendicular}}}}{{{\text{Hypotenuse}}}} = \frac{{AE}}{{AC}} \cr
& \Rightarrow \sin {30^ \circ } = \frac{6}{{AC}} \cr
& \Rightarrow \frac{1}{2} = \frac{6}{{AC}} \cr
& \Rightarrow AC = 2 \times 6 = 12 \cr
& \therefore {\text{Length of AC}} = 12\,m \cr} $$
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Let AB and CD be two poles
AB = 20 m, CD = 14 m
A and C are joined by a wire
CE || DB and angle of elevation of A is 30°
Let CE = DB = x and AC = L
Now AE = AB - EB = AB - CD = 20 - 14 = 6 m
$$\eqalign{
& {\text{Now in right }}\Delta ACE, \cr
& \sin \theta = \frac{{{\text{Perpendicular}}}}{{{\text{Hypotenuse}}}} = \frac{{AE}}{{AC}} \cr
& \Rightarrow \sin {30^ \circ } = \frac{6}{{AC}} \cr
& \Rightarrow \frac{1}{2} = \frac{6}{{AC}} \cr
& \Rightarrow AC = 2 \times 6 = 12 \cr
& \therefore {\text{Length of AC}} = 12\,m \cr} $$
Was this answer helpful ?
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