Question

A plane flies 545 kilometers with a bearing of 316° from Naples to Elgin (see figure). The plane then flies 680 kilometers from Elgin to Canton (Canton is due west of Naples). Find the bearing of the flight from Elgin to Canton. (Round to the nearest whole number.)

Answer 1

Answer:

• 235°

Step-by-step explanation:

• Use of low of sines
• Consider triangle CEN
• Bearing of angle counted from zero to the vector of flight

We have

• ∠CNE = complementary with 44° ⇒ m∠CNE = 90° - 44° = 46°
• NE = b = 545 km
• EC = a = 680 km
• ∠ECN = x

Find the  measure of angle x:

• sin 46° / a = sin x / b
• sin 46° / 680 = sin x / 545
• sin x = 545 sin 46 deg / 680
• x = arcsin (545 sin 46 deg / 680)
• x = 35° (rounded)

Bearing of the flight from Elgin to Canton is:

• 270° - 35° = 235° as the vector is in the third quadrant