Answer:
≈ 9.197 feet (rounded to the nearest hundredth)
Step-by-step explanation:
The LAW OF COSINES says:
[tex]c^{2} = a^{2} + b^{2} - 2ab * cos(c)[/tex]
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:
[tex]c^{2} = 8^{2} + 12^{2} - 2(8)(12) * cos(50)[/tex]
[tex]c^{2} = 64 + 144 - 192 * 0.64278760[/tex] you can find cos(50°) in a calculator.
make sure it's set on degrees and not radians.
[tex]c^{2} = 208 - 123.4152192[/tex]
[tex]c^{2} = 84.5847808[/tex]
[tex]c = \sqrt{84.5847808}[/tex]
≈ 9.197 feet
