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

Answer:

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:

$c^{2}$ = $a^{2}$ + $b^{2}$ - 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 = $\sqrt{126.857}$

  = 11.2631

x ≅ 11

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