Answer:
B = 55°
a ≈ 143
c ≈ 212
Step-by-step explanation:
From the triangle above we are given a triangle with two known angles and a known side. The sum of angles in a triangle is 180°. Since we are given two angles, the last angle can be gotten when you subtract the two known angles from 180°. Therefore,
angle B = 180° - 42° - 83°
angle B = 55°
To find side a we can use law of sine
a/sin A = b/sin B
a/sin 42° = 175/sin 55°
a/0.66913060635 = 175/0.81915204428
cross multiply
0.81915204428
a = 117.097856113
divide both sides by 0.81915204428
a = 117.097856113
/0.81915204428
a = 142.950087143
a ≈ 143
To find side c
b/sin B = c/sin C
175/sin 55 = c/sin 83°
cross multiply
c sin 55° = 175 sin 83°
divide both sides by sin 55°
c = (175 × 0.99254615164)/0.81915204428
c = 173.695576537 / 0.81915204428
c = 212.043146019
c ≈ 212
