SOLUTION: Given triangle ABC with b=6 c=9 and A=146, what is the length of a?

Question 199231: Given triangle ABC with b=6 c=9 and A=146, what is the length of a?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
as we know two adjacent sides and included angle, we can find remaining side using
law of cosines
.
a^2 = b^2 + c^2 - 2 bc cos theta
.
a^2 = 6^2 + 9^2 - 2 * 6 * 9 *cos 146
.
a^2 = 36 +81 + 89.536 = 206.54
.
a= 14.37
.
checking using law of sines
.
14.37/sin 146 = 25.700 = 6 / sin B = 9 / sin C
.
sin B = 6 / 25.7 =.2335 ,,,, B=13.5 deg
.
sin C = 9/25.7 =.3502 ,,,,C = 20.5 deg
.
A + B + C = 146 +13.5 + 20.5 = 180,,,,ok
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