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.
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