Two tracking stations are on the equator 115 miles apart. A weather balloon is located on a bearing of N 40degrees E from the western station and on a bearing N 15degrees E from the eastern station. How far is the balloon from the western station?

Matonya

Matonya

Answered question

2022-08-05

Two tracking stations are on the equator 115 miles apart. A weather balloon is located on a bearing of N 40degrees E from the western station and on a bearing N 15degrees E from the eastern station. How far is the balloon from the western station?

Answer & Explanation

Siena Bennett

Siena Bennett

Beginner2022-08-06Added 17 answers

Imagine the three points as a triangle.
Let w = western station angle (angle between eastern station andballoon at western station), e = eastern station angle (anglebetween western station and balloon at eastern station), B =balloon angle (angle between eastern and western station atballoon).
W = 50 (90-40) degrees
E = 105 (90 + 15)) degrees
Therefore, B = 25 (180 - (105 + 55)) degrees.
Using the sine laws:
a / sin A = b / sin B = c / sin C
Where A, C, and C are the angles of any triangle, and a, b, c, arethe respective angle's opposite sides (e.g. side a is oppositeangle A on the triangle).
So transform to the pronumerals used above (W, E, B):
w / sin W = e / sin E = b / sin B
We need to find the distance from the western station ( e, as is itopposite the angle at the eastern station ), so disregard e / sin E(as we have 3 of the 4 of e, E, b, and B). Remember that the lengthgiven between the 2 stations is side b (as it is opposite theballoon on the triangle).
e / sin E = b / sin B
e = b sin E / sin B
e = 115 sin ( 105 ) / sin ( 25 )
w = 262.84 miles
The answers is number 3, 263 miles

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