Question

Jenny walks 4km on a bearing 052 degree . She changes direction and walks a further 5 km to finish due east of her starting point . Find how far jenny is from starting point.

Answer 1

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Answer on Question #62990 – Math – Trigonometry

Question

Jenny walks 4km on a bearing 052 degree. She changes direction and walks a further 5 km to finish due east of her starting point. Find how far jenny is from starting point.

Solution

First displacement is 4 km 52 degree north of east. Second displacement is 5 km east. Let $y$ be the north direction and $x$ be the east direction.

$$d_{1x} = 4 \cos 52{}^\circ$$ $$d_{1y} = 4 \sin 52{}^\circ$$ $$d_{2x} = 5$$ $$d_{2y} = 0$$

Total displacement has coordinates:

$$d_x = 5 + 4 \cos 52{}^\circ$$ $$d_y = 4 \sin 52{}^\circ$$

The distance from starting point is

$$d = \sqrt{(5 + 4 \cos 52{}^\circ)^2 + (4 \sin 52{}^\circ)^2} = 8.1 \text{ km}.$$

Answer: 8.1 km.