Answer :
The distance between the weather tracking station and the balloon can be
found by triangulation.
The distance from the balloon to the western station is approximately 646.4 miles
Reasons:
The given parameters are;
Distance between the two stations = 146 miles
Location of the weather balloon from the Western station = N35°E
Location of the weather balloon from the Eastern station = N23°E
The location of the station = On the equator
Required:
The distance of the balloon from the Western station
Solution:
- The angle formed between the horizontal, and the line from the Western station to the balloon = 90° - 35° = 55°
- The angle formed between the horizontal, and the line from the Eastern station to the balloon = 90° + 23° = 113°
The angle at the vertex of the triangle formed by the balloon and the two stations is 180° - (55 + 113)° = 12°
By sine rule, we have;
[tex]\dfrac{146}{sin(12^{\circ})} = \dfrac{Distance \ from \ balloon \ to \ western \ station}{sin(113^{\circ})}[/tex]
Therefore;
[tex]Distance \ from \ balloon \ to \ western \ station}{}=\dfrac{146}{sin(12^{\circ})} \times sin(113^{\circ}) \approx 646.4[/tex]
The distance from the balloon to the Western station is approximately 646.4 miles.
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