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Find all angles A,C,AC

Find all angles A,C,AC-example-1
User Evinje
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Answer:

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. soooo 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 , :)

User Jon Coombs
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