9514 1404 393
Answer:
24.1
Step-by-step explanation:
The third angle is C = 180° -55° -19° = 106°. The law of sines can be used to find the other two sides:
a/sin(A) = c/sin(C) ⇒ a = c(sin(A)/sin(C))
b/sin(B) = c/sin(C) ⇒ b = c(sin(B)/sin(C))
Then the sum of the lengths of the sides is ...
P = a + b + c = c(sin(A)/sin(C)) +c(sin(B)/sin(C)) +c
= c(1 +(sin(A) +sin(B))/sin(C)) = 11(1 +(0.8192 +0.3256)/0.9613)
≈ 11(1 +1.1909) ≈ 24.0994
The perimeter of the triangle is about 24.1 units.
