A jet leaves Reno, Nevada and is headed toward Miami, Florida at a bearing of 100°. The distance between the two cities is approximately 2472 miles. (a) How far north and how far west is Reno relative to Miami? (Round your answers to two decimal places.) miles north miles west (b) If the jet is to return directly to Reno from Miami, at what bearing should it travel? °

Question

Mathematics

Payne

23 January, 20:13

A jet leaves Reno, Nevada and is headed toward Miami, Florida at a bearing of 100°. The distance between the two cities is approximately 2472 miles. (a) How far north and how far west is Reno relative to Miami? (Round your answers to two decimal places.) miles north miles west (b) If the jet is to return directly to Reno from Miami, at what bearing should it travel? °

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Answers (1)

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Chace · Answer 1

Answers:

(a) 429.26 mi N and 2434.44 mi W; (b) 280°

Step-by-step explanation:

A compass bearing of 100° (E by S) is 10° south of 90°.

The jet is flying the hypotenuse of a right triangle.

(a) Distances from Miami

sin10 = OM/2472

OM = 2472sin10 = 2472 * 0.173 648 = 429.26 mi

OR = 2472cos10 = 2472 * 0.984 8077 = 2434.44 mi

Reno is 2434.44 mi west and 429.26 mi north of Miami

(b) Return bearing

Bearing = 100 + 180 = 280°

For the return flight, the jet should fly a bearing of 280° (W by N).