AAS Triangle

In the triangle, the given angles and side is:
∠A = 110°
∠B = 40°
Side a = 8
Step 1:
Using the angle sum theorem, we will find the missing angle, ∠C
∠A + ∠B + ∠C = 180°, here ∠A = 110°, ∠B = 40°
110° + 40° + ∠C = 180°
∠C = 180° – (110° + 40°)
∠C = 30°
Step 2:
Now, we will find side b using the Law of Sines
a/sin A = b/sin B, here ∠A = 110°, a = 8, ∠B= 40°
8/ sin (110°) = b/ sin (40°)
b = sin (40°) x 8/ sin (110°)
b = 0.64 x 8/0.93
b = 5.50
Similarly, we will find side c using the Law of Sines
b/sin B = c/sin C, here b = 5.50, ∠B= 40°, ∠C = 30°
5.50/sin 40° = c/sin 30°
c = 5.50 x sin 30°/ sin 40°
c = 5.50 x 0.5/0.64
c = 4.29
This is to note as a rule that it is always better to use the sides and angles that are given to us rather than ones we have just worked out.

The given triangle is also an AAS triangle having angles and side:
∠B = 100°
∠C = 50°
Side b = 10.5
Step 1:
Using the angle sum theorem, we will find the missing angle, ∠A
∠A + ∠B + ∠C = 180°, here ∠B = 100°, ∠C = 50°
∠A + 100° + 50° = 180°
∠A = 180° – (100° + 50°)
∠A = 30°
Step 2:
Now, we will find side c using the Law of Sines
b/sin B = c/sin C, here b = 10.5, ∠B = 100°, ∠C = 50°
10.5/sin 100° = c/sin 50°
c = 10.5 x sin 50°/ sin 100°
c = 10.5 x 0.76/0.98
c = 8.14
Similarly, we will find side a using the Law of Sines
a/sin A = b/sin B, here ∠A = 30°, b = 10.5, ∠B = 100°
a/sin 30° = 10.5/sin 100°
a = sin 30° x 10.5/ sin 100°
a = 0.5 x 10.5/0.98
a = 5.35

Option (1) and (2)