Solve ΔABC. (Round your answers to the nearest degree. If there is no solution, enter NO SOLUTION.)

Question

Solve ΔABC. (Round your answers to the nearest degree. If there is no solution, enter NO SOLUTION.)

a = 10,    b = 15,    c = 13

𝛼 =	°
𝛽 =	°
𝛾 =	°

Answer 1

use law of cosines to find an angle:

c^2 = a^2 + b^2 - 2*a*b*cos(gamma)

13^2 = 10^2 + 15^2 - 2*10*15*cos(gamma)

0,.52 = cos(gamma)

58.67 = gamma

use law of sines to find another angle after finding gamma:

sin(gamma) = sin(beta)

---------------- -----------

c b

sin(58.67) = sin(beta)

-------------- ------------

13 15

0.85 * 15 = sin(beta)*13

sin(beta) = 0.98

beta = 78.52

alpha = 180 - 78.52 - 58.67 = 44.81