13. find the value of x.

Explanation:

Step1: Recall the tangent function

In a right - triangle, (\tan\theta=\frac{\text{opposite}}{\text{adjacent}}). For (\angle C = 50^{\circ}), the side opposite to (\angle C) is (AB=x) and the side adjacent to (\angle C) is (BC = 8). So, (\tan C=\frac{AB}{BC}).

Step2: Substitute the values

Since (C = 50^{\circ}) and (BC = 8), we have (\tan50^{\circ}=\frac{x}{8}).

Step3: Solve for (x)

Multiply both sides of the equation (\tan50^{\circ}=\frac{x}{8}) by (8). We know that (\tan50^{\circ}\approx1.191753592). So, (x = 8\times\tan50^{\circ}\approx8\times1.191753592\approx9.5).

Answer:

(x\approx9.5)