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?

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vijayalalitha vijayalalitha · Answer 1 · 2020-02-11T08:23:06+01:00

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,

[tex]\frac{a}{sin a} = \frac{b}{sin b}[/tex]

Let us substitute the values.

Where [tex]a=x, sin a= sin 112[/tex] and [tex]b=165, sin b = sin 18[/tex]

Thus, we have,

[tex]\frac{x}{sin 112} =\frac{165}{sin 18}[/tex]

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

[tex]x=sin 112(\frac{165}{sin 18} )[/tex]

Simplifying, we have,

[tex]x=0.9272(533.98)\\x=495[/tex]

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