Answer:
1.73 units.
Step-by-step explanation:
We have been given that in triangle PTC measure of angle T is 120 degrees and measure of angle C is 30 degrees. We are asked to find the length of side PC.
We will use law of sines to solve for side PC.
[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a ,b and c are opposite sides to angle A, B and C.
Upon substituting our given values in law of sines, we will get:
[tex]\frac{PC}{\text{sin}(120^{\circ})}=\frac{PT}{\text{sin}(30^{\circ})}[/tex]
[tex]\frac{PC}{\text{sin}(120^{\circ})}*\text{sin}(120^{\circ})=\frac{4}{\text{sin}(30^{\circ})}*\text{sin}(120^{\circ})[/tex]
[tex]PC=\frac{4}{0.5}*0.866025403784[/tex]
[tex]PC=2*0.866025403784[/tex]
[tex]PC=1.732050807568[/tex]
[tex]PC\approx 1.73[/tex]
Therefore, the length of side PC is approximately 1.73 units.
