Answer: Approximately 28 km
The more accurate, yet still approximate value, is roughly 27.995735464379
Round that however you need to.
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Explanation:
As the diagram shows, the uppercase letters A,B,C represent the corner points of the triangle. They also represent the angles. The diagram says that:
The missing angle C is....
A+B+C = 180
C = 180-A-B
C = 180-59-91
C = 30
which we'll use later.
Convention usually has the side lengths be lowercase letters 'a', b, and c. Those lowercase letters are opposite their uppercase counterpart. We'll have side 'a' opposite angle A, then b is opposite B, and c is opposite C. This allows us to quickly label a triangle and find the missing sides and/or angles. The phrasing "solve the triangle" basically means "find all the missing sides and angles". For this problem, we're only concerned with one side.
The diagram says that side c = 14 due to it being opposite angle C.
The goal is to find side b, which is the shorter way of saying "find AC".
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From here, we can use the law of sines to find side b
b/sin(B) = c/sin(C)
b/sin(91) = 14/sin(30)
b = sin(91)*14/sin(30)
b = 27.995735464379 which is approximate
b = 28
Side AC is roughly 28 km long.
I rounded to the nearest whole number since the "14 km" is also a whole number. Your teacher may want you to round differently.
Make sure your calculator is in degree mode.
