Question

For a rope course and climbing wall, a guy wire R is attached 47 ft high on a vertical pole. Another guy wire S is attached 40 ft above the ground on

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asked 2021-05-26
For a rope course and climbing wall, a guy wire R is attached 47 ft high on a vertical pole. Another guy wire S is attached 40 ft above the ground on the same pole. Find the angle α between the wires if they are attached to the ground 50 ft from the pole.

Answers (2)

2021-05-27

Let x be the angle of the smaller right triangle and y be the angle of the larger right triangle so that:
\(α=y−x\)
For the smaller right triangle with hypotenuse as guy wire S, we can use the tangent ratio to find x:
\(\displaystyle{\tan{{x}}}=\frac{{40}}{{50}}\)
\(\displaystyle{x}={{\tan}^{{-{{1}}}}{\left(\frac{{40}}{{50}}\right)}}\)
\(\displaystyle{x}\sim{38.66}°\)
For the larger right triangle with hypotenuse as guy wire R, we can use the tangent ratio to find y
\(\displaystyle{\tan{{y}}}=\frac{{47}}{{50}}\)
\(\displaystyle{y}={{\tan}^{{-{{1}}}}{\left(\frac{{47}}{{50}}\right)}}\)
\(\displaystyle{y}\sim{43.23}°\)
Hence, \(\displaystyleα={43.23}°−{38.66}°\)
\(α \approx 4.57^{\circ}\)

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Best answer
2021-08-11

Answer is given below (on video)

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