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A guide wire of length 108 meters runs from the top of an antenna to the ground. If the angle of elevation to the top of the antenna is 42.3 degrees, then what is the height of the antenna

Sagot :

jessmzhou4

Answer: Approximately 72.69 meters

Step-by-step explanation:

  • Antenna height = h

[tex]sin(42.3)=\frac{opposite}{hypotenuse} =\frac{h}{108} \\\\108*sin(42.3)=h\\\\h=72.685[/tex]

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The height of the antenna by using the Pythagoras theorem is 72.68 meters.

What is trigonometry?

"Trigonometry is one of the branches of mathematics that deals with the relationship between the sides of a triangle (right triangle) with its angles".

For the given situation,

Length of guidewire = 108 meters

Angle of elevation = 42.3 degrees

Height of the antenna be 'h'.

By Pythagoras theorem,

[tex]Sine[/tex] θ = [tex]\frac{Perpendicular}{hypotenuse}[/tex]

On substituting the above values,

⇒ [tex]Sine 42.3 = \frac{h}{108}[/tex]

⇒ [tex]0.6730 =\frac{h}{108}[/tex]

⇒ [tex]h=0.6730[/tex] × [tex]108[/tex]

⇒ [tex]h= 72.68[/tex]

Hence we can conclude that the height of the antenna is 72.68 meters.

Learn more about trigonometry here

https://brainly.com/question/13971311

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