The tops of two poles with height 25 m and 35 m are connected by a wire which is inclined to the horizontal at an angle of 30^{0}. Find the length of the wire.

Foundation

Mathematics Foundation

Introduction to Trigonometry

Properties of Triangle

Some Applications of Trigonometry

Question

The tops of two poles with height 25 m and 35 m are connected by a wire which is inclined to the horizontal at an angle of 30

^{0}

. Find the length of the wire.

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Given that, the tops of two poles with height

25 m

and

35 m

are connected by a wire which is inclined to the horizontal at an angle of

3 0^{0}

To find out: The length of the wire.

Based on the given information, we can draw the figure shown above.

A E = 25 B D = B C + C D = 35 ∴ B C = 35 - 25 = 10

I n △ A B C, \sin 3 0^{0} = \frac{B C}{A B} = \frac{10}{A B} [∵ \sin θ = \frac{Opposite Side}{Hypotenuse}]

A B = \frac{10}{\frac{1}{2},} [∵ \sin 3 0^{0} = \frac{1}{2}]

= 20

∴

Length of wire

(A B) = 20 m

Hence, the length of the wire connecting the two poles is

20 m