Two weather tracking stations are on the equator 165 miles apart. a weather balloon is located on a bearing of n 40°e from the western station and on a bearing of n 22°e from the eastern station. how far is the balloon from the western station?

The distance from balloon to the western station is 495 miles.

Explanation:

The distance between two weather stations are 165 miles.

The angle of the regular triangle bearing from the western station is given by

90° - 40° = 50°

The angle of the regular triangle bearing from the eastern station is given by

90° + 22° = 112°

The angle of the balloon is given by

180° - 50° - 112° = 18°

Now, to find the distance of the balloon from the western station, let us use the law of sines formula,

Let us substitute the values.

Where and

Thus, we have,

Multiplying both sides of the equation by sin 112, we get,

Simplifying, we have,

Thus, the distance from balloon to the western station is 495 miles.

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