Question

two helicopters leave a heliport at the same time. the first flies 110 km/h in a direction of 280 degrees. the second flies 260 km/h in a direction of 260 degrees. after 2 hours, how far apart are the helicopters? round your answer to the nearest kilometer.

Explanation:

Step1: Calculate the distances each helicopter has flown

The distance formula is \(d = vt\).
For the first helicopter: \(v_1 = 110\space km/h\), \(t = 2\space h\), so \(d_1=110\times2 = 220\space km\)
For the second helicopter: \(v_2 = 260\space km/h\), \(t = 2\space h\), so \(d_2=260\times 2=520\space km\)

Step2: Find the angle between their paths

The angle \(\theta\) between the two directions: \(\theta=280^{\circ}-260^{\circ} = 20^{\circ}\)

Step3: Use the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 220\), \(b = 520\), \(C = 20^{\circ}\)

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Answer:

\(321\space km\)