Solve the problem.
-The locations, given in polar coordinates, of two planes approaching an airport are $\left( 9 \mathrm { mi } , 20 ^ { \circ } \right)$ and $\left( 2 \mathrm { mi } , 71 ^ { \circ } \right)$. Find the distance between the two planes.
A) $\approx 7.9 \mathrm { mi }$
B) $\approx 51.48 \mathrm { mi }$
C) $\approx 9.22 \mathrm { mi }$
D) $\approx 8.42 \mathrm { mi }$

Question

Solve the problem.
-The locations, given in polar coordinates, of two planes approaching an airport are $\left( 9 \mathrm { mi } , 20 ^ { \circ } \right)$ and $\left( 2 \mathrm { mi } , 71 ^ { \circ } \right)$. Find the distance between the two planes.
A) $\approx 7.9 \mathrm { mi }$
B) $\approx 51.48 \mathrm { mi }$
C) $\approx  9.22 \mathrm { mi }$
D) $\approx 8.42 \mathrm { mi }$

Quizplus · Accepted Answer

To find the distance between two points in polar coordinates $(r_1, \theta_1)$ and $(r_2, \theta_2)$, we use the formula $d = \sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos(\theta_1 - \theta_2)}$. Plugging in the given values, we get $d \approx 7.9 \, \mathrm{mi}$.

Solve the Problem (9mi,20∘)\left( 9 \mathrm { mi } , 20 ^ { \circ } \right)(9mi,20∘)

Solve the Problem $\left( 9 \mathrm { mi } , 20 ^ { \circ } \right)$