Question

Find the length of the third side of a triangular garden if two sides measure 8 feet and 12 feet and the included angle measures 50​°​.

Answer 1

Answer:

≈ 9.197 feet  (rounded to the nearest hundredth)

Step-by-step explanation:

The LAW OF COSINES says:

$c^{2} = a^{2} + b^{2} - 2ab * cos(c)$

We can use it to solve problems like this where we need to find a side given two sides and an angle ("SAS").

Let's plug in our givens to this equation:

$c^{2} = 8^{2} + 12^{2} - 2(8)(12) * cos(50)$

$c^{2} = 64 + 144 - 192 * 0.64278760$      you can find cos(50°) in a calculator.

                                                         make sure it's set on degrees and not                                                                   radians.

$c^{2} = 208 - 123.4152192$

$c^{2} = 84.5847808$

$c = \sqrt{84.5847808}$

≈ 9.197 feet