Question

Andrea and Carlos left the airport at the same time. Andrea flew at 190 mph on a course with bearing of 80°, and Carlos flew at 240 mph on a course with a bearing of 210°.
How far apart were they after 4 hours?
__mi
(Round to the nearest tenth)

Answer 1

Answer on Question # 41854 – Math – Trigonometry

Andrea and Carlos left the airport at the same time. Andrea flew at 190 mph on a course with bearing of 80°, and Carlos flew at 240 mph on a course with a bearing of 210°.

How far apart were they after 4 hours?

Solution:

$$\begin{array}{l} \angle \alpha = 80{}^{\circ}, \angle \beta = 210{}^{\circ} \\ \angle CAB = \angle \beta - \angle \alpha = 130{}^{\circ} \\ \end{array}$$

AB – distance which flew Andrea

AC – distance which flew Carlos

$$AB = 190 * 4 = 760 \text{ km}, AC = 240 * 4 = 960 \text{ km}$$

We need to find BC:

Use the law of cosines in the triangle CAB:

$$\begin{array}{l} CB^{2} = CA^{2} + BA^{2} - 2 * AB * AC * \cos \angle CAB \approx 577600 + 921600 - \\ -1459200 * (-0.642787609) \approx 2437155.679 \\ \end{array}$$ $$CB = \sqrt{2437155.679} \approx 1561.1 \text{ km}$$

Answer: 1561.1 km

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