Answer:
18.7
Step-by-step explanation:
First find the degree of J which is 6 (found this by doing 180=160+14=6
so then you make the fraction J/sin14=8.1/sin6
cross multiply so its Jsin6=8.1sin14
to get J by itself you divide by sin 6 so
J=8.1sin14 divided by sin6 which equals 18.7
The length of [tex]l[/tex] is approximately 18.8 inches.
In this question we know the value of two angles, in sexagesimal degrees, and a length of the triangle, in inches, we must determine the length [tex]l[/tex] by the law of sine:
[tex]\frac{l}{\sin \angle L} = \frac{j}{\sin \angle J}[/tex] (1)
[tex]\angle J = 180^{\circ} - \angle K - \angle L[/tex] (2)
If we know that [tex]j = 8.1\,in[/tex], [tex]\angle K = 160^{\circ}[/tex] and [tex]\angle L = 14^{\circ}[/tex], then the length of [tex]l[/tex] is:
[tex]\angle J = 180^{\circ}-160^{\circ}-14^{\circ}[/tex]
[tex]\angle J = 6^{\circ}[/tex]
[tex]l = j\cdot \left( \frac{\sin \angle L}{\sin \angle J} \right)[/tex]
[tex]l = (8.1\,in)\cdot \left(\frac{\sin 14^{\circ}}{\sin 6^{\circ}} \right)[/tex]
[tex]l \approx 18.8\,in[/tex]
The length of [tex]l[/tex] is approximately 18.8 inches.
We kindly invite to check this question on law of sine: https://brainly.com/question/17289163
