How far is the balloon from the western station?

Question

Two tracking stations are on the equator 121 miles apart. A weather balloon is located on a bearing of N 38 degrees from the western station and on a bearing of n 22 degrees E from eastern station. How far is the balloon from the western station?

Answer 1

The distance between the weather tracking station and the balloon can by solved using the Geometry triangle method.

The given math problem factors:

Distance between the two stations = 121 miles apart

Location of the weather balloon from the Western station = N 38 degrees

Location of the weather balloon from the Eastern station = N 22 degrees

Solution: The distance of the balloon from the Western station 407.0175687 miles ( roundoff answer as specified)

The angle formed between the horizontal, and the line from the Western station to the Balloon is

90 degrees - 38 degrees = 52 degrees

The angle formed between the horizontal and the line from the Eastern station to the Balloon =

90 degrees + 22 degrees = 112 degrees

The angle at the vertex of the triangle formed by the balloon and the two stations is

180 degrees - (52+112) degrees = 16 degrees

By using the Sine Rule:

121 Distance from balloon to western station

Sin (16 degrees)

Distance from balloon to western station=

121 multiply by Sin (112 degrees) =.9271838546

Sin (16 degrees)

121 divided by .2756373558 = 438.9825887 multiply by .9271838546 = 407.0175687 miles roundoff answer as specified

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.