
Step-by-step solution:

The figure is shown above:
Notice that:
triangle ABD is a Right Triangle:
\sin{D}=\frac{AB}{AD}
Substitute the AD=130, angle D=74 degree into the Sine:
\sin{(\textcolor{secondary}{74^{\circ}})}=\frac{{AB}}{\textcolor{primary}{130}}
cross multiply we get,
AB=\sin{(74^{\circ})}\times130=>AB\approx125
Similarly, For cosine:
\cos{D}=\frac{BD}{AD}
Substitute the AD=130, angle D=74 degree into the Cosine:
\cos{(\textcolor{secondary}{74^{\circ}})}=\frac{{BD}}{\textcolor{primary}{130}}
cross multiply we get,
BD=\cos{(74^{\circ})}\times130=>BD\approx36
Notice that triangle ABC is a Right Triangle:
tangent formula (tan(x)):
\tan{C}=\frac{AB}{BC}
Substitute the AB= 125,BC= (36+x), angle C=42 degree into the Tangent:
\tan{(\textcolor{secondary}{42^{\circ}})}=\frac{{\textcolor{primary}{125}}}{\textcolor{tertiary}{36+x}}
After simplifying we get,
x\approx103
The value of x is approximately 103.
You may be like this post: