Question

An airplane departs city A and travels at a bearing of 100°. City B is directly south of city A. When the plane is 200 miles east of city B, how far has the plan traveled? How far apart are city A and City B?

Answer 1

Answer on Question #44183, Math, Trigonometry

An airplane departs city A and travels at a bearing of $100{}^{\circ}$. City B is directly south of city A. When the plane is 200 miles east of city B, how far has the plan traveled? How far apart are city A and City B?

Solution.

$$\cos 10{}^{\circ} = \frac{x}{y};$$ $$\sin 10{}^{\circ} = \frac{200}{y} \Rightarrow y = 200 \sin 10{}^{\circ};$$ $$x = y \cos 10{}^{\circ} = 200 \sin 10{}^{\circ} \cos 10{}^{\circ} = 100 \sin 20{}^{\circ};$$

How far apart are city A and City B? Answer: $x = 100 \sin 20{}^{\circ}$.

how far has the plan traveled? Answer: $y = 200 \sin 10{}^{\circ}$.

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