Theory:

Let us learn how to construct a triangle if the measures of \(2\) of its sides and the angle between them are known. To construct a triangle, first we shall draw a rough diagram which gives an idea where the sides would be. Let us consider an example.
Example:
Consider a triangle \(ABC\) whose sides are \(AB = 4 \ cm\), \(BC = 6 \ cm\) and \(\angle ABC = 120^{\circ}\).
 
Solution:
 
Step 1: First, we shall draw the rough figure of the triangle \(ABC\) with the given measurements.
 
12.PNG
 
Step 2: Draw a line segment \(BC\) of length \(6 \ cm\).
 
13.PNG
 
Step 3: Place the protractor at \(B\), draw \(\angle CBX\) making an angle of \(120^{\circ}\).
 
14.PNG
 
Step 4: With \(B\) as centre, draw an arc of radius \(4 \ cm\) which cuts \(BX\) at \(A\).
 
15.PNG
 
Step 5: Draw a line joining the points \(A\) and \(C\).
 
16.PNG
 
Thus, \(ABC\) is the required triangle.