Find the missing parts of the triangle Round to the nearest

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. C = 122.2degree a = S km b = 10.4 km c = 22 km, A = 22.5degree, B = 35.3degree No triangle satisfies the given conditions. c = 19.1 km, A = 26.5degree, B = 31.3degree c = 16.2 km, A = 24.5degree, B = 33.3degree

Solution

C = 122.2 deg ; a= 8 km ; b = 10.4km

use the cosine rule to find c:

c^2 = a^2 +b^2 -2a*bcosC

=8^2 +10.4^2 -2*8*10.4cos122.2

c = 16.15 = 16.2 km

Use sine rule : a/sinA = c/sinC

sinA = a*sinC/c = 8*sin122.2/16.2 =0.4178

A = 24.69 = 24.7 deg

B = 180 -A -C = 33.1 deg

So, we can see last option is approximately has same solution