Question

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

Answer 1

`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`