SOLUTION: Adam, Betty, and Charlie are standing on a field. From Adam’s point of view, the angle between Betty and Charlie is 28°. From Charlie’s point of view, the angle between Betty

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Question 1050555: Adam, Betty, and Charlie are standing on a field.
From Adam’s point of view, the angle between Betty and Charlie is 28°.
From Charlie’s point of view, the angle between Betty and Adam is 48°.
Adam and Charlie are 15.5 metres apart. How far is Adam standing from Betty?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Adam, Betty, and Charlie are standing on a field.
From Adam’s point of view, the angle between Betty and Charlie is 28°.
From Charlie’s point of view, the angle between Betty and Adam is 48°.
Adam and Charlie are 15.5 metres apart.
How far is Adam standing from Betty?
:
Draw this triangle, ABC, label the sides opposite each angle a,b,c
A = 28 degrees
C = 48 degrees
Find B
180 - 28 - 48 = 104 degrees
side b = 15.5 m
side c = the dist between A & B
:
Use the law of sines
c%2Fsin%28C%29 = b%2Fsin%28B%29
Using the given values
c%2Fsin%2848%29 = 15.5%2Fsin%28104%29
c%2F.743 = 15.5%2F.970
Cross multiply
.970c = 15.5 * .743
.970c = ll.512
c = 11.512%2F.970
c = 11.87 m from A to B