Find all angles A, C,AC

Step-by-step explanation:

They say  "solve" the triangle,  means just find all the sides and all the angles is all they are asking by "solve"   .. saying "solve" sounds so ominous  :/  like.. good luck with this... nobody can do it..  :D ..  which there are math questions like that.  s anyway,  let's find AC , I'll call is side b , then using law of cosines, where AC = b  , a = 9 and c=21, and angle B = 91°,  then

b = sq rt[ a^2+c^2 - 2*a*c*cos(B) ]

b = sq rt[ 9^2 +21^2 -2*9*21*cos(91)]

b = sq rt [ 81 +441 -378 * (-0.0174524 )]

b = sq rt [ 522 + 6.597]

b = sq rt [528.597]

b = 22.991

side AC = 23.0  ( rounded to nearest 10th)

now that we have all three sides lets use law of sines to solve the angles, b/c it's easier  :P    call me "lazy"  maybe ?    or call me "maybe"   :D :D  the song, ofc.   :D anyway

sin(91) / 22.991 = sin(C) /21

arcSin [ 21*sin(91) / 22.991] = C

arcSin[ 0.91326 ] = C

65.96 ° = C

C = 66.0 °

and then the same for angle A

Sin(91)/22.991 = sin(A) / 9

arcSin [ 9* sin(91) / 22.991 ] = A

arcSin [ 0.3913979 ] =A

23.04 ° = A

A = 23.0 °

let's add up the 3 angles to see if we get 180 or very very close

180.0015 °  ohh that's pretty close , nice I think the answers are right :P

23 +66+91=180  so the rounding to the nearest 10th makes them perfect , great ,  :)

step-by-step explanation:

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