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22 votes
22 votes
Se the Law of Sines or the Law of Cosines to solve for the indicated measure.

(3 points)
b
a
A
B
C
(Diagram not drawn to scale)
a = 29.7, c = 24.3, and b = 10.1.
Find mA.
13

User Rkenmi
by
3.3k points

1 Answer

24 votes
24 votes

Answer:


m\angle A\approx112.72^\circ

Explanation:

Since only side lengths are given and no angles, we are forced to use the Law of Cosines. The equation to find angle A is
\displaystyle \cos(A)=(b^2+c^2-a^2)/(2bc):


\displaystyle \cos(A)=(b^2+c^2-a^2)/(2bc)\\\\\cos(A)=(10.1^2+24.3^2-29.7^2)/(2(10.1)(24.3))\\\\A=\cos^(-1)\biggr((10.1^2+24.3^2-29.7^2)/(2(10.1)(24.3))\biggr)\\\\A\approx112.72^\circ

User Brian Marick
by
3.2k points