Question

Convert rectangular coordinates (7200, 5400) to polar coordinates

Answer 1

To convert the rectangular coordinates (7200, 5400) to polar coordinates, find the radial distance (9000 m) using the Pythagorean theorem and the angle (36.87°) using the arctangent function.

Step-by-step explanation:

To convert rectangular coordinates to polar coordinates, you need to find the radial distance to the origin (r) and the angle (θ) that line makes with the positive x-axis. The radial distance can be found using the Pythagorean theorem:

r = √(x² + y²)

And the angle can be determined using the arctangent function:

θ = arctan(y/x)

In the case of the coordinates (7200, 5400), we calculate r as:

r = √(7200² + 5400²) = √(51840000 + 29160000) = √81000000 ≈ 9000 m

And θ as:

θ = arctan(5400/7200) = arctan(3/4) ≈ 36.87°

So, the polar coordinates are approximately (9000 m, 36.87°).