Question

Use the Law of Cosines to solve each triangle with the given measures. Round answers to the nearest tenths. a = 0.48 yd, b = 0.63 yd, c = 0.75 yd

Answer 1

According to the Law of Cosines,
cosine (A) = (b^2 + c^2 - a^2) / (2 * b * c)
cosine (A) = (.63^2 + .75^2 -.48^2) / (2*.63*.75)
cosine (A) = (.3969 + .5625 -.2304) / .945
cosine (A) = .729 / .945
cosine (A) = 0.7714285714
The arc cosine of ( 0.7714285714) =  39.518 Degrees
Angle A = 39.518 Degrees

For the next angle it is easier to use the Law of Sines
a / sin (A) = b / sin (B) = c / sin (C)

.48 / sin (39.518) = .63 / sin (B)

sin (B) = .63 * sin (39.518) / .48

sin (B) = (.63 * 0.63632) / .48

sin (B) = 0.4008816 / .48

sin (B) = 0.83517

Angle B = 56.634 Degrees

Angle C is easily solved by:

Angle C = 180 -39.518 -56.634
 
Angle C = 83.848

Yes, it's just that "simple".  LOL