A pole has two wires attached to it, one on

Edmund Adams 2021-11-28 Answered
A pole has two wires attached to it, one on each side, forming two right triangles as shown.
image

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Expert Answer

Marlene Broomfield
Answered 2021-11-29 Author has 8187 answers

Step 1
Given that:
A pole has two wires attached to it, one on side forming two right triangles as shown,
From the figure,
Length of pole = OB
\(\displaystyle\angle{O}{A}{B}={41}^{{\circ}}\)
\(\displaystyle\angle{O}{B}{A}={90}^{{\circ}}\)
\(\displaystyle{A}{B}={34}{f}{t}\)
length of wire 1= OA
Step2
Part A
To calculate the length of pole,
In \(\triangle OAB\),
\(\displaystyle{\frac{{{P}{e}{r}{p}{e}{n}{d}{i}{c}ul{{a}}{r}}}{{{B}{a}{s}{e}}}}={\tan{{\left({41}^{{\circ}}\right)}}}\)
\(\displaystyle{\frac{{{O}{B}}}{{{A}{B}}}}={\tan{{\left({41}^{{\circ}}\right)}}}\)
\(\displaystyle{O}{B}={A}{B}\times{\tan{{\left({41}^{{\circ}}\right)}}}\)
\(\displaystyle={34}\times{\tan{{\left({41}^{{\circ}}\right)}}}\)
\(\displaystyle={29.56}{f}{t}\)
Hence the poll is 29.56 ft tall
Step3
Part B
To calculate the length of wire 1,
Apply Pythagoras theorem in triangle OAB,
In \(\triangle OAB\),
\(\displaystyle{\left({O}{A}\right)}^{{{2}}}={\left({O}{B}\right)}^{{{2}}}+{\left({A}{B}\right)}^{{{2}}}\)
\(\displaystyle={\left({29.56}\right)}^{{{2}}}+{\left({34}\right)}^{{{2}}}\)
\(\displaystyle={873.7936}+{1156}\)
\(\displaystyle{\left({O}{A}\right)}^{{{2}}}={2029.7936}\)
\(\displaystyle{O}{A}=\sqrt{{{2029.7936}}}\)
\(\displaystyle{O}{A}={45.05}{f}{t}\)
Hence wire 1 is 45.05 ft long

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