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The tops of two poles of height $18$ m and $10$ m are connected by wire. If the wire makes an angle of measure $45^{o}$ with the horizontal, then the length of wire is

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16

18

8 \sqrt{2}

8

answer is A.

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Detailed Solution

It is given that the tops of two poles of height

18

m and

10

m are connected by wire & it makes an angle of measure

45^{o}

with the horizontal.
We have to find the length of the wire.
Now, let us assume that the pole having height

18 m

be AB and

CD

be the pole of height

10 m

Since, we know that,

AE = AB - EB

[DC = EB]

\Rightarrow AE = 18 - 10 = 8 m

△ ADE,

\sin 30^{\circ} = \frac{AE}{AD}

\Rightarrow \frac{1}{2} = \frac{8}{AD}

[since

\sin 30^{\circ} = \frac{1}{2}

]

\Rightarrow AD = 2 \times 8

\Rightarrow AD = 16 m

Hence, the length of the wire is

16 m

.
Therefore, the correct option is 1.

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