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find c in an oblique triangle wih a= 10 b= 6 and angle A= 30 with law of sines

0 votes

You need to use the law of sines and at first find all the angles in the triangle with the law of sines, and later find side c

asked Nov 22, 2013 in TRIGONOMETRY by abstain12 Apprentice
reshown Nov 22, 2013 by goushi

1 Answer

0 votes

Given sides a = 10, b = 6 angle A = 30

Use law of sines

a/SinA = b/SinB = c/SinC -----> (1)

Now ignore c/SinC in (1)

a/SinA = b/SinB

10/Sin30 = 6/SinB

10/0.5 = 6/SinB

20 = 6/SinB

Dvide to each side by 6.

20/6 = 6/6SinB

3.33 = 1/SinB

Cross multiplication.

SinB =1/3.333

SinB = 0.30003

B = Sin^-1(0.3003)

B = 17.45

Now we know two anglesof triangle ,let's find out C

C = 180-(A+B)

C = 180-(30+17.45)

C = 180-47.45

C = 132.55

Now ignore a/SinA in (1).

b/SinB = c/SinC

6/0.3003 = c/Sin(132.55)

19.98 = c/0.7366

c = 19.98(0.7370)

c = 14.71

answered Jan 25, 2014 by friend Mentor

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