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

Circles
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 &alpha; between the wires if they are attached to the ground 50 ft from the pole.

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, $$\displaystyleα={43.23}°−{38.66}°$$
$$α \approx 4.57^{\circ}$$

2021-08-11

Answer is given below (on video)