Question

An observation tower is 65m high. A support wire is attached to the tower 30m from the top. If the support wire and the ground form an angle of 56 degrees, what is the length of the support wire, to the nearest tenth?

Answer 1

The support wire is the hypotenuse of the right triangle formed. Therefore, the length of the support wire is 42.2 meters.

The situation forms a right angle triangle.

Right angle triangle

A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, the height of the tower where the wire was attached is the opposite side of the triangle formed.

The wire was attached 30 m from the top. Hence, 65m - 30m = 35 m.

Therefore,

sin 56° = opposite / hypotenuse

sin 56° = 35 / x

The hypotenuse is the length of the support wire.

Therefore,

x = 35 / 0.82903757255

x = 42.2195416164

x = 42.2 m

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