Two Planes Leave an Airport $\newline$ This is the only question in this section. $\newline$ Question $\newline$ Two planes leave the same airport at the same time. One flies at a bearing of $N 20^{\circ} E$ at $500$ miles per hour. The second flies at a bearing of $S 30^{\circ} E$ at $600$ miles per hour. How far apart are the planes after $2$ hours? Round answer to the nearest mile. $\newline$ Answer Altempt $3$ out of $20$ $\newline$ Additional Solution $\newline$ No Solution $\newline$ $12711$ miles $\newline$ Submit Answer $\newline$ Copwridut $02024$ DeltaMatheom All Rights Reserved. Privacy Policy I Terms of Service

Full solution

Q. Two Planes Leave an Airport

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This is the only question in this section.

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Question

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Two planes leave the same airport at the same time. One flies at a bearing of

N 20^{\circ} E

500

miles per hour. The second flies at a bearing of

S 30^{\circ} E

600

miles per hour. How far apart are the planes after

2

hours? Round answer to the nearest mile.

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Answer Altempt

3

out of

20

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Additional Solution

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No Solution

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12711

miles

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Submit Answer

\newline

Copwridut

02024

Calculate Plane Distances: Calculate the distance each plane travels in extdollar{} $2$ extdollar{} hours. $\newline$ First plane: extdollar{} $500$ ext{ miles/hour} imes $2$ ext{ hours} = $1000$ ext{ miles}. extdollar{} $\newline$ Second plane: extdollar{} $600$ ext{ miles/hour} imes $2$ ext{ hours} = $1200$ ext{ miles}. extdollar{}
Use Law of Cosines: Use the Law of Cosines to find the distance between the planes. $\newline$ The angle between the paths of the planes is $20^\circ + 30^\circ = 50^\circ$ . $\newline$ $\text{Distance}^2 = 1000^2 + 1200^2 - 2 \times 1000 \times 1200 \times \cos(50^\circ)$ .
Calculate Cosine and Distance: Calculate the cosine of $50$ degrees and then the distance. $\newline$ $\cos(50^\circ) \approx 0.6428$ . $\newline$ $\text{Distance}^2 = 1000^2 + 1200^2 - 2 \times 1000 \times 1200 \times 0.6428$ .
Perform Calculation: Perform the calculation. $\newline$ $\text{Distance}^2 = 1,000,000 + 1,440,000 - 2 \times 1000 \times 1200 \times 0.6428$ . $\newline$ $\text{Distance}^2 = 2,440,000 - 1,542,720$ . $\newline$ $\text{Distance}^2 = 897,280$ .
Find Final Distance: Take the square root to find the distance. $\newline$ Distance $\approx \sqrt{897,280}$ . $\newline$ Distance $\approx 947$ miles.