Question 194101
right  triangle  means  pythagorous  theorem  holds,,,,,c^2=a^2+b^2
finding  c  from  given  two  legs,
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c^2 = 24^2 + 32^2 =1600
c=40
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rough  sketch  of  triangle  helps.  Label  vertex  opposite  side  with  same  letter,  but  capital.
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sin A =  opposite/hyp = 24 /40  =  .6,,,,,arc  sin  a=  36.9  deg
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tan a = opposite / adjacent = 24/32 = .75,   arc  tan a = 36.9 deg
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other  problem
again  use  c^2 = a^2  + b^2
46^2 = 35.4^2 + b^2
b^2 = 46^2-35.4^2
b^2=862.8
b = 29.4
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,Last  problem
again,  a  sketch  helps  keep  everything  straight
sum  of  angles  =  180,  therefore  find  last  angle,  180-90-41.8 =48.2  deg
sin  of  48.2  =  2.8 / c
c=2.8 / sin 48.2 = 3.756
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sin  41.8 = b/3.756
b=3.756 * sin 41.8  = 2.5 
therefore  all  angles  and  all  sides  are  labeled
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