SOLUTION: using law of sines, find all missing measurements in the triangle JSR angle J= 36 degrees side JS= 72 side RS= 48

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Question 250733: using law of sines, find all missing measurements in the triangle JSR
angle J= 36 degrees
side JS= 72
side RS= 48
Found 2 solutions by JimboP1977, drk:
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
The law of sines states: a%2Fsin+A+=+b%2Fsin+B+=+c%2Fsin+C where a,b,c are the lengths of the triangle and A, B, C are the angles opposite the sides.
48%2FSin+36+=+72%2FSin+angle+R
72%2F%2848%2FSin+36%29+=+Sin+angle+R
Sin-1+%2872%2ASin+36%2F48%29+=++angle+R
61.84=angle+R
We know that the interior angles of a triangle always add up to 180 so angle S must be 180-36-61.84=82.16
side+S%2FSin+82.16+=+48%2F+Sin+36
side+S+=+48%2ASin+82.16%2FSin+36
side+S+=+80.9

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Law of sines states
a%2FsinA+=+b%2FsinB+=+c%2FSinC
Notice that after draw the picture angle J and side RS are connected. We have
48%2Fsin%2836%29+=+72%2Fsin%28R%29
sin%28R%29+=+72sin%2836%29%2F48
Using trig tables or a calculator, we get
R ~ 61.85 degrees.
Since angles add to 180, S = 82.15 degrees
--
using law of sines again, we can find side JR
48%2Fsin%2836%29+=+JR%2Fsin%2882.15%29
JR+=+48%2Asin%2882.15%29%2Fsin%2836%29
JR ~ 80.9
angle J: 36
angle R: 61.85
angle S: 82.15
side JS: 72
side JR: 80.9
side RS: 48