Question

Two planes leave the same airport at the same time. one flies at 30° east of north at 400 miles per hour. the second flies at 40° east of south at 500 miles per hour. how far apart are the planes after 3 hours?

Answer 1

To find the distance between the planes after 3 hours, calculate the distances each plane has traveled and use the Law of Cosines.

Step-by-step explanation:

To find the distance between the planes after 3 hours, we first need to calculate the distances each plane has traveled in 3 hours.

For the first plane:

Distance = Speed × Time = 400 miles/hour × 3 hours = 1200 miles.

For the second plane:

Distance = Speed × Time = 500 miles/hour × 3 hours = 1500 miles.

Now, we can use the Law of Cosines to find the distance between the planes:

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

d^2 = (1200)^2 + (1500)^2 - 2(1200)(1500)*cos(30°)

d^2 = 1440000 + 2250000 - 3600000*(√3/2)

d^2 = 3690000 - 3600000*(√3/2)

d^2 = 3690000 - 1800000*√3

d ≈ √(3690000 - 1800000*√3) ≈ 932.48 miles.