Question

Suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120°. What is the length of the third side of the triangle?

A. 58.04
B. 47.43
C. 33.60
D. 53

Answer 1

Answer:

A. 58.04°

Step-by-step explanation:

Let the sides of the triangle be A , B  and C.

A = 32

B = 35

C = what we don't know.

The opposite angle to C is 120° and its just denoted as ∡C

The formula to find C² = A² + B² - 2ABcos∡C

C² = 32² + 35² - 2(32)(35)cos120°

C² = 1024 + 1225 - 2240cos120°

C² = 3369

C = $\sqrt{3369}$ ≅ 58.04°