Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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]

View image jessmzhou4

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

#SPJ2

View image KarpaT
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.