Question

Round answer to two significant digits.

House B is located at a bearing of N67°E from house A. House C is 495 meters from house A at a bearing of S68°E. House B is located at a bearing of N11°W from house C. Find the distance from house A to house B

Answer 1

Answer on Question #45509 – Math - Trigonometry

Round answer to two significant digits.

House B is located at a bearing of N67°E from house A. House C is 495 meters from house A at a bearing of S68°E. House B is located at a bearing of N11°W from house C. Find the distance from house A to house B.

Solution.

$$\angle BAC = 180{}^{\circ} - 67{}^{\circ} - 68{}^{\circ} = 45{}^{\circ},$$ $$\angle ACB = 68{}^{\circ} - 11{}^{\circ} = 57{}^{\circ}$$ $$\angle ABC = 180{}^{\circ} - 57{}^{\circ} - 45{}^{\circ} = 78{}^{\circ}$$

Now use Law of sines to determine side AB:

$$\frac{AB}{\sin 57{}^{\circ}} = \frac{AC}{\sin 78{}^{\circ}} \rightarrow AB = \frac{AC \sin 57{}^{\circ}}{\sin 78{}^{\circ}} = \frac{495 * 0.839}{0.978} \approx 425 \, \text{m}.$$

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