Question

A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that 40 m from the base of the antenna. If the wire makes an angle of 58deg 20min with the group find the length of the wire.

Answer 1

The length of the wire is 76.19 m.

Explanation:

It is given that a guy wire is attached to the top of a radio antenna and to a point on horizontal ground that 40 m from the base of the antenna.

It means base of the right angled triangle is 40 m.

The wire makes an angle of 58deg 20min with the ground.

1 degree = 60 min

Using this conversion convert the given angle in degree.

`58^(\circ)20'=58^(\circ)(20)/(60)^(\circ)=58(1)/(3)^(\circ)=(175)/(3)^(\circ)`

In a right angled triangle

`\cos \theta=(adjacent)/(hypotenuse)`

`\cos ((175)/(3)^(\circ))=(40)/(hypotenuse)`

`0.525=(40)/(hypotenuse)`

`hypotenuse=(40)/(0.525)`

`hypotenuse=76.190`

Therefore the length of the wire is 76.19 m.