Question

- Using satellite technology, the distance between two planes can be measured by keeping track of the angle between them and the distance of each plane to the tracking station.
Assume plane 1 is 225.57 miles away, plane 2 is 196.18 miles away and the angle formed with the tracking station is 41.47°. How far apart are the planes? Round your answer to two decimal places.

Answer 1

first draw out a picture

Answer 2

we want to find the distance x

Answer 3

so use the law of cosines

c^2 = a^2 + b^2 - 2ab*cos(C)

x^2 = 225.57^2 + 196.18^2 - 2*225.57*196.18*cos(41.47)

keep going to solve for x

Answer 4

so x=114.83?

Answer 5

no

Answer 6

x^2 = 225.57^2 + 196.18^2 - 2*225.57*196.18*cos(41.47)

x^2 = 225.57^2 + 196.18^2 - 2*225.57*196.18*0.749303

x^2 = 50881.8249 + 38486.5924 - 2*225.57*196.18*0.749303

x^2 = 50881.8249 + 38486.5924 - 66316.7961622957

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x = ??

Answer 7

x=151.827?

Answer 8

much better

Answer 9

Awesome, thanks!

Answer 10

so it rounds to 151.83

Answer 11

Okay, thanks for the help! I appreciate it

Answer 12

yw