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

Answer:

The length of the wire is 76.19 m.

Step-by-step 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.

$58^{\circ}20'=58^{\circ}\frac{20}{60}^{\circ}=58\frac{1}{3}^{\circ}=\frac{175}{3}^{\circ}$

In a right angled triangle

$\cos \theta=\frac{adjacent}{hypotenuse}$

$\cos (\frac{175}{3}^{\circ})=\frac{40}{hypotenuse}$

$0.525=\frac{40}{hypotenuse}$

$hypotenuse=\frac{40}{0.525}$

$hypotenuse=76.190$

Therefore the length of the wire is 76.19 m.