Question

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 N29.1degrees​E, and the bearing from B to A is N60degreesE. The bearing from A to B is S60degrees​W, 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?

Answer 1

Answer:

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!!!