A wire is attached to the top of a radio antenna and to a point on horizontal ground that is 50m form the base of the antenna. If the wire makes an angle of 60 with the ground, approximate the length of the wire.*A. 25 mB. 25√3 mC. 50√3 mD. 100 m
Question
A wire is attached to the top of a radio antenna and to a point on horizontal ground that is 50m form the base of the antenna. If the wire makes an angle of 60 with the ground, approximate the length of the wire.*A. 25 mB. 25√3 mC. 50√3 mD. 100 m
Solution
The problem can be solved using trigonometry, specifically the sine function.
The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the angle is 60 degrees, the opposite side is the height of the antenna, and the hypotenuse is the length of the wire.
We can set up the equation as follows:
sin(60) = height / wire_length
We know that sin(60) = √3 / 2 and the height is 50m. We can substitute these values into the equation:
√3 / 2 = 50 / wire_length
Solving for wire_length gives:
wire_length = 50 / ( √3 / 2 ) = 50 * 2 / √3 = 100 / √3 ≈ 57.74m
None of the options A, B, C, D match this result. Please check the problem statement again.
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