Answer:
x = 133.33°
Step-by-step explanation:
The Law of Cosines
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]
Since we know the values of all three side lengths, we solve the equation for x:
[tex]\displaystyle \cos x=\frac{a^2+b^2-c^2}{2ab}[/tex]
For the triangle in the figure: a=4.1, b=8.5, c=11.7, x=angle C. Applying the formula:
[tex]\displaystyle \cos x=\frac{4.1^2+8.5^2-11.7^2}{2*4.1*8.5}[/tex]
[tex]\displaystyle \cos x=\frac{-47.83}{69.7}[/tex]
[tex]\displaystyle \cos x=-0.6862[/tex]
[tex]x = \arccos (-0.6862)[/tex]
x = 133.33°
