Answer:
120.62 feet
Step-by-step explanation:
Let the entrance be the origin (0,0). If the Ferris wheel is located 95 feet east and 156 feet north of the entrance, its coordinates are (95, 156). If the swings are located 23 feet west and 124 feet north of the entrance, its coordinates are (-23, 124).
We now find the distance from the swing to the Ferris wheel which for a pair of coordinates (x₁, y₁) and (x₂, y₂) is gotten from d = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (-23, 124) and (x₂, y₂) = (95, 156).
So, d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(95 - (-23))² + (156 - 124)²]
= √[(95 + 23))² + (156 - 124)²]
= √[(118)² + (32)²]
= √[13924 + 1024]
= √14948
= 122.26 feet
Since Jalen is standing exactly three-eights the distance from the Ferris wheel to the swings, his distance from the Ferris wheel is d' = 3d/8 = 3 × 122.26/8 = 45.85 feet
To find the coordinates (x', y') of Jalen's point from the entrance, we subtract his distance from the Ferris wheel from the coordinates of the point of the Ferris wheel. So, (x', y') = (95 - 45.85, 156 - 45.85) = (49.15, 110.15).
So, Jalen's distance from the entrance is gotten from
d = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (0, 0) and (x₂, y₂) = (49.15, 110.15).
So, d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(49.15 - 0)² + (110.15 - 0)²]
= √[(49.15)² + (110.15)²]
= √[2,415.7225 + 12,133.0225]
= √14,548.745
= 120.62 feet
