Question

In a circus, a guy wire A is attached to the top of a 30-ft pole. Wire B is used for performers to walk up to the tight wire, 10 ft above the ground.

Circles
ANSWERED
asked 2021-05-31
In a circus, a guy wire A is attached to the top of a 30-ft pole. Wire B is used for performers to walk up to the tight wire, 10 ft above the ground. Find the angle ϕ between the wires if they are attached to the ground 40 ft from the pole.

Answers (1)

2021-06-01

Let x be the angle of the smaller right triangle and y be the angle of the larger right triangle so that:
\(\displaystyleϕ={y}−{x}\)
For the smaller right triangle with hypotenuse as guy wire B, we can use the tangent ratio to find x:
\(\displaystyle{\tan{{x}}}=\frac{{10}}{{40}}\)
\(\displaystyle{x}={{\tan}^{{-{{1}}}}{\left(\frac{{10}}{{40}}\right)}}\)
\(\displaystyle{x}\sim{14.04}°\)
For the larger right triangle with hypotenuse as guy wire A, we can use the tangent ratio to find y:
\(\displaystyle{\tan{{y}}}=\frac{{{30}+{10}}}{{40}}\)
\(\displaystyle{\tan{{y}}}={1}\)
\(y=\tan^{-1}*1\)
\(y=45^{\circ}\)
Hence, \(\displaystyleϕ={45}°−{14.04}°\)
\(\displaystyleϕ≈{30.96}°\)

0
 
Best answer

expert advice

Need a better answer?
...