In triangle abc, m∠a=55 triangle abc, m∠a=55°, c=11c=11, and m∠b=19m∠b=19°. find the perimeter of the triangle

First, we illustrate the problem as shown in the picture. By convention, we denote capital letters as angles and the small letters as opposite sides to those respective angles. We can find the perimeter of the triangle by adding all it sides. So, the next step is to find sides a and b.

Since a triangle has a total of 180° in interior angles, then angle C can be solved by

180° = A + B + C
C = 180° - 55° - 19°
C = 106°

Next, we use the Law of Sines. This law can be used in any type of triangle. This law states that there is a fixed ratio of side to sine of the opposite angle. In equation, that would be written as

a/sin A = b/sin B = c/sin C

Since, we know already side c and angle C, the fixed ratio is then,

11/sin 106° = 11.443

The last step is to apply ratio and proportion:

11.433 = a/sin 55°
a = 9.37 units

11.433 = b/sin 19°
b = 3.73 units

Thus, the perimeter of the triangle is 
P = a + b + c
P = 9.37 +3.73 +11
P = 24.1 units