Answer: B = 43.9 , b = 18 71 , c = 8.45
Explanation:
from the law of sine,
a b c
--------- = ---------- = ----------- a =25.3, C = 18.2 degree, A = 110.8 deg.
Sine A Sine B Sine C
to get the value of c,
a c
--------- = -----------
Sine A Sine C,
25.3 c
----------- = -------------
Sine 110.8 Sine 18.2
Now cross multiply to get the value of c
c x Sine 110.8 = 25.3 x Sine 18.2
Therefore c = 25.3 x Sine 18.2
------------------------
Sine 110.8
checking for Sine 18.2 in your log tables/calculators , ie, sine 18 under 2, = 0.3123 and sine 110.8 = 0.9348
c = 25.3 x 0.3123
--------------------
0.9348
= 8.45.
To get angle B, sum total of a triangle is supplementary ie, 180 degree.
meaning that A + B + C = 180
Therefore, angle B = 180 - ( 110.8 + 25.3)
= 180 - 136.1
= 43.9
Now to find b,
b c
------------- = ------------
Sine B Sine C
b 8.45
--------- = ------------
Sine 43.9 Sine 18.2
b x sine 18.2 = 8.45 x Sine 43.9
b = 8.45 x 0.6934
--------------------
0. 3123
b = 18.708
= 18.71.
The final Answer = B = 43.9, b = 18.71, c = 8.45