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In triangle abc angle 30a+ 6b=5c determine angle a ,angle b and angle c.Can the answer please be given in full detail.

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by iamryanjay

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by iamryanjay

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30 A + 6 B = 5 C we know C = 180 - A - B

35 A + 11 B - 900 = 0

5 * (7 A - 180) = 11 B

On both sides we have prime numbers... So B has to be a multiple of 5. and (7A - 180) must be a multiple of 11.

5 * (7 A - 180) = 11 * (5 n)

=> 7 A - 180 = 11 * n

=> 7 A = 25 * 7 + 7 * n + (5 + 4 n)

thus 5 + 4 n must be a multiple of 7....

n = 4, 11, 18 will satisfy this condition.

A = (11 *n + 180)/ 7 gives angles 32°, 43°, 54° respectively

B = 20°, 55°, 90° respectively

then C = 180 - A - B = 138 deg, 82, 36 respectively.

35 A + 11 B - 900 = 0

5 * (7 A - 180) = 11 B

On both sides we have prime numbers... So B has to be a multiple of 5. and (7A - 180) must be a multiple of 11.

5 * (7 A - 180) = 11 * (5 n)

=> 7 A - 180 = 11 * n

=> 7 A = 25 * 7 + 7 * n + (5 + 4 n)

thus 5 + 4 n must be a multiple of 7....

n = 4, 11, 18 will satisfy this condition.

A = (11 *n + 180)/ 7 gives angles 32°, 43°, 54° respectively

B = 20°, 55°, 90° respectively

then C = 180 - A - B = 138 deg, 82, 36 respectively.

30A/30 = 6B/30 = 5C/30

THEN,

A/1 = B/5 =C/6

A:B:C =1:5:6

1x

<A=15X 1 =15DEGREE

<B =15X 5= 75 DEGREE

<C=15X 6 +90 DEGREE