Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance of about 456.2 miles. A second flight option flies first to city C and then connects to A. The bearing from B to C is N29.1degreesE, and the bearing from B to A is N60degreesE. The bearing from A to B is S60degreesW, and the bearing from A to C is N78.3degreesW. How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight?

The amount of frequent flyer miles Adam will receive if he takes the connecting flight rather than the direct flight = 107.34 miles

Step-by-step explanation:

The sketch of Adam's journey from city B through C and then A is shown in the attached image to.this question.

Using Sine rule, we can obtain the unknown distances BC and CA

In sine rule notation,

BA = c = 456.2 miles

BC = a = ?

CA = b = ?

Angle A = 41.7°

Angle B = 30.9°

Angle C = 107.4°

Sin rule is that

[(Sin A)/a] = [(Sin B)/b] = [(Sin C)/c]

[(Sin A)/a] = [(Sin C)/c]

(Sin 41.7°)/a = (Sin 107.4°)/456.2

a = 456.2 × (Sin 41.7°) ÷ (Sin 107.4°)

a = 318.03 miles

[(Sin B)/b] = [(Sin C)/c]

(Sin 30.9°)/b = (Sin 107.4°)/456.2

b = 456.2 × (Sin 30.9°) ÷ (Sin 107.4°)

b = 245.51 miles

Hence,

BC = 318.03 miles

CA = 245.51 miles

Total flyer miles covered by taking the connecting flight = 318.03 + 245.51 = 563.54 miles.

The difference between the total miles covered by taking the connecting flight and by taking the direct flight = 563.54 - 456.2 = 107.34 miles.

Hope this Helps!!!

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