1Solve for the remaining sides and angles if possible if not

1)Solve for the remaining sides and angles if possible (if not, answer \"DNE\" in all answer boxes). As in the text, (A,a),(B,b), and (C,c) are angle-side opposite pairs. Round to one decimal places, if necessary.

(a) a=7, b=9, C=55°
A=___°
B=___°
C=___°
a=___
b=___
c=___

(b) A=97°, b=28, c=40
A=___°
B=___°
C=___°
a=___
b=___
c=___

(c) a=8, b=14, c=18
A=___°
B=___°
C=___°
a=___
b=___
c=___

(d)a=2, b=5, c=9
A=___°
B=___°
C=___°
a=___
b=___
c=___

Solution

(a) a=7, b=9, C=55°

Apply cosine rule :

c^2 = a^2 + b^2 - 2abcosC

c^2 = 7^2 + 9^2 - 2*7*9cos65

= 76.75

c = 8.76 = 8.8

apply sin rule : b/sinB = c/sinC

sinB = b*sinC/c = 9*sin55/8.8 = 0.837

B = 56.9 deg

A = 180 - B - C = 180 - 56.9 -55 = 68.1 deg