240,030 views
44 votes
44 votes
In ABC, M2A = 55°, c = 11, and m2B = 19º. Find the perimeter of the triangle.

User Oalders
by
2.4k points

1 Answer

18 votes
18 votes

9514 1404 393

Answer:

24.1

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.

In ABC, M2A = 55°, c = 11, and m2B = 19º. Find the perimeter of the triangle.-example-1
User David Benitez Riba
by
2.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.