Question

Use the Pythagorean Theorem, and the properties of right triangles to model an equation that fits the problem. One of the cables that anchors the center of the London Eye Ferris wheel to the ground must be replaced. The center of the Ferris wheel is 69.5 meters above the ground, and the second anchor on the ground is 23 meters from the base of the Ferris wheel. Approximately how long is the cable, and what is the angle of elevation (from ground up to the center of the Ferris wheel)

Answer 1

73.21 m

71.68°

Explanation:

Like the question has stated, we're to solve this using Pythagoras theorem.

Pythagoras theorem states that

opp² + adj² = hyp²

From the question, we're asked to find the hypotenuse, being given the opposite side and the adjacent. The opposite side is the center of the Ferris wheel above the ground, and that is 69.5 m. While the adjacent is the distance of the second anchor.

Succinctly put, we have

69.5² + 23² = hyp²

4830.25 + 529 = hyp²

hyp² = 5359.25

hyp = √5359.25

hyp = 73.21 meters.

Therefore, the length of the cable is 73.21 meters long.

To get the angle, we use the formula

Sin Φ = opp/hyp

Sin Φ = 69.5 / 73.21

Sin Φ = 0.9493

Φ = sin^-1 0.9493

Φ = 71.68°

Therefore, the angle of elevation to the center of the Ferris wheel is 71.68°