The value of x in the triangle is approximately 29.8 degrees.
Identify the given information:
Angle A = 74°
Side BC = 39 (opposite to angle A)
Side AC = 12 (adjacent to angle A)
Choose an appropriate trigonometric ratio to relate the given sides and the unknown angle:
Since you have a side opposite to the unknown angle and a side adjacent to the unknown angle, you can use the tangent function (tan).
Apply the tangent function:
tan(A) = opposite side / adjacent side
tan(74°) = 39 / 12
Solve for the unknown angle:
Using a calculator, you get approximately 2.984.
Round to the nearest tenth of a degree:
x ≈ 29.8°
Therefore, the value of x in the triangle is approximately 29.8 degrees.