Given the triangle below, describe TWO ways one could go about solving for the variable x.

Question

(3 points per valid method)
Then solve for x. (2 points)
A
X
10.3
37°
B
C

Answer 1

Method 1: Using the Law of Sines
1. Set up the equation using the Law of Sines: sin(A)/a = sin(B)/b = sin(C)/c.
2. Substitute the known values: sin(37°)/10.3 = sin(B)/x.
3. Solve for x: x = (10.3sin(37°))/sin(B).

Method 2: Using the exterior angle theorem
1. Calculate the exterior angle at C: 180° - 37° = 143°.
2. Since the exterior angle is equal to the sum of the two remote interior angles, we have: x = 143° - 10.3°.

Solving for x:
Method 1:
x = (10.3sin(37°))/sin(B) = (10.3sin(37°))/sin(143°) ≈ 8.53.

Method 2:
x = 143° - 10.3° = 132.7°.