Two sides of a triangle measure 8 ft and 12 ft, respectively. The included angle is 65˚. Approximately how long is the third side of the triangle?

Approximately 11 feet.

Step-by-step explanation:

Let the length of the third side of the triangle be represented by x. Applying Cosine rule, we have:

= + - 2abCos C

⇒ = + - 2(8 x 12) Cos

       = 64 + 144 - 192 x 0.42262

       = 208 - 81.143

       = 126.857

x =

  = 11.2631

x ≅ 11

The length of the third side of the triangle is approximately 11 feet.

i believe

step-by-step explanation:

from my conclusion c