A wire achoring a telephone pole to the ground is 175 feet long. the angle of elevation from the ground to the top pole is 50 degrees. how tall is the telephone pole ?

1 Answer
Ben
Jun 12, 2018

The pole is approximately 112.5 feet tall

Explanation:

If the guideline is 175ft long and makes a 50-degree angle with the earth, AND we assume the pole makes a 90-degree angle with the earth, we have ourselves a right triangle!

The wire is the hypotenuse of the triangle, and the pole is the side opposite of the angle. Using our knowledge of trig:

#"sine"="opposite"/"hypotenuse"#

We can use that relationship as follows:

#sin(50)=h/175#

where #h# is the height of the pole. Let's solve for #h#:

#175sin(50)=h#

#color(green)(h=112.4878317~=112.5#

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