Final answer:
To find the Cartesian coordinates of points in polar coordinates, use x = r * cos(θ) and y = r * sin(θ). The Cartesian coordinates for the given points are (2.165, 1.25) and (-1.9, 3.291), and their distance is 4.85 meters.
Step-by-step explanation:
To find the Cartesian coordinates of a point given in polar coordinates, we can use the formulas:
- x = r * cos(θ)
- y = r * sin(θ)
For the given points, (2.5 m, 30°) and (3.8 m, 120°), we can substitute the values into these formulas to find their Cartesian coordinates:
- x₁ = 2.5 * cos(30°) = 2.165
- y₁ = 2.5 * sin(30°) = 1.25
- x₂ = 3.8 * cos(120°) = -1.9
- y₂ = 3.8 * sin(120°) = 3.291
Therefore, the Cartesian coordinates of the points are: (2.165, 1.25) and (-1.9, 3.291).
To find the distance between the points, we can use the distance formula:
distance = sqrt((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the coordinates into this formula, we get:
distance = sqrt((-1.9 - 2.165)² + (3.291 - 1.25)²)
= 4.85 meters