Answer:
1. x = 6.8; 2. x = 24.2
Step-by-step explanation:
1.
With the letters you drew and given, to find side x, the Law of Cosines can be set up as follows:
[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] -2bc * cosA
Next, substitute the values for the sides and angle:
[tex]a^{2}[/tex] = [tex]9^{2}[/tex] + [tex]8^{2}[/tex] - 2(9)(8)cos47º
Simplify:
[tex]a^{2}[/tex] = 145 - 144cos47º
Finally, take the square root of both sides:
a = 6.8
2.
With the letters you drew and given, to find side x, the Law of Cosines can be set up as follows:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab * cosC
Next, substitute the values for the sides and angle:
[tex]c^{2}[/tex] = [tex]17^{2}[/tex] + [tex]13^{2}[/tex] - 2(17)(13)cos107º
Simplify:
[tex]c^{2}[/tex] = 458 - 442cos107º
Finally, take the square root of both sides:
c = 24.2
