A village is 10 km on a bearing $$ 050^{\circ} $$ from a point O . Calculate how far the village is north of O .

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To find how far the village is north of point O, we need to calculate the distance between the village and point O in the north direction.

Given:
- The village is 10 km on a bearing of $$ 050^{\circ} $$ from point O.

To find the distance in the north direction, we can use trigonometry. Since the bearing is $$ 050^{\circ} $$, it means the angle between the north direction and the line connecting the village to point O is $$ 50^{\circ} $$.

Let's denote the distance in the north direction as $$ d $$. We can use the cosine function to find $$ d $$ since the cosine of an angle in a right-angled triangle is the ratio of the adjacent side to the hypotenuse.

The formula to find the distance in the north direction is:
$$ d = 10 \times \cos(50^{\circ}) $$

Now, we can calculate the distance in the north direction.
The distance in the north direction from the village to point O is approximately 9.65 km.
The village is approximately 9.65 km north of point O.

A village is 10 km on a bearing from
a point O . Calculate how far the village is
north of O .

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A village is 10 km on a bearing from a point O . Calculate how far the village is north of O .