Question 204845
(1)  sum  of  angles  in  triangle  is  180 degrees
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78 +x +x =180,,x= 51 degrees, ( 2 legs @ 8 cause  isosceles  triangle  with  base  angles  the  same)
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check (sin 78 / 10) = .0978,,,(sin 51 / 8 = .0971),,,,ok  (obeys  law  of  sines)
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(2)  Please  check  to  see  that  problem  is  correct
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sum  of  angles,,(63 + 54 +x ) =180,,,cause  x  to  be  63.
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With  the  base  opposite  vertex, it  conflicts  with  law  of  sines, to  have  base  smaller  than  sides.
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if base  angles  are  63,and  sides  are  10,,,sin 63 /10 = .0891..
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the  side  opposite  the  54 degree  angle  is  ,,sin 54/x = .0891,,,or  x=9.08
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Again,,  please  review  the  problem