Question

The locations, given in polar coordinates, for two planes approaching an airport are (4 mi, 12_) and (3 mi, 73_). Find the distance between the two planes.

a. 1.00 mi
c. 5.00 mi
b. 61.01 mi
d. 3.66 mi

Answer 1

Use formula for the distance between two points with polar coordinates.
`A(r_1,\theta_1),B(r_2,\theta_2) \\d= \sqrt{r_1^2+r_2^2-2r_1r_2cos{(\theta_1-\theta_2)}} \\ \\A(4,12^o),B(3,73^o) \\d= \sqrt{4^2+3^2-2* 4* 3* cos{(73^o-12^o)}} \\d= \sqrt{25-24* cos{61^o}} \\d= \sqrt{25-24* cos{61^o}} \\d \approx 3.66`