Explanation:
Using the modified picture attached to this answer;
Parameters
x = Angle X
8 = x
19 = y
14 = z
Therefore,
Using Cosine rule
x² = y² + z² - 2·y·z·cos X
Masking Cos X the subject of the formula,
Cos X = (y² + z² - x²) / (2·y·z)
Cos X = (19² + 14² - 8²) / (2·19·14)
Cos X = (361 + 196 - 64) / 532
Cos X = (557 -64) / 532
Cos X = 493 / 532
Cos X = 0.92669
But, since we are looking for angle X, we have to divide both sides by Cos, therefore having;
X = Cos-¹ [0.92669]
Since 1 / Cos = Cos-¹
Therefore,
X = 22.075
And since x, our unknown, is equal to angle X, then,
x = 22.1 (to the nearest tenth)