Question

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?

Answer 1

Approximately 11 feet.

Explanation:

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

`c^(2)` =
`a^(2)` +
`b^(2)` - 2abCos C

⇒
`x^(2)` =
`8^(2)` +
`12^(2)` - 2(8 x 12) Cos
`65^(o)`

= 64 + 144 - 192 x 0.42262

= 208 - 81.143

= 126.857

x =
`√(126.857)`

= 11.2631

x ≅ 11

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