Answer:
[tex]45.6=x[/tex]
Step-by-step explanation:
We can use law of cosines since three sides are given and we are asked to find an angle.
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]
Angle [tex]C[/tex] is the angle that is opposite to the side [tex]c[/tex].
So here [tex]x[/tex] is our Angle [tex]C[/tex] and the side opposite to that is 11 which makes it [tex]c[/tex] for this formula.
This means [tex]a=8[/tex] and [tex]b=15[/tex] (or other way around-doesn't matter).
Let's plug in:
[tex]11^2=8^2+15^2-2(8)(15)\cos(x)[/tex]
Simplify the terms with exponents:
[tex]121=64+225-2(8)(15)\cos(x)[/tex]
Perform the multiplication next to the trig function:
[tex]121=64+225-240\cos(x)[/tex]
Add 64 and 225:
[tex]121=289-240\cos(x)[/tex]
Our goal is to isolate the trig function.
Subtract 289 on both sides:
[tex]121-289=-240\cos(x)[/tex]
Simplify left hand side:
[tex]-168=-240\cos(x)[/tex]
Divide both sides by -240:
[tex]\frac{-168}{-240}=\cos(x)[/tex]
Simplify left hand side:
[tex]0.7=\cos(x)[/tex]
Take cosine's inverse on both side:
[tex]\cos^{-1}(0.7)=x[/tex]
Type left hand side into calculator:
[tex]45.6=x[/tex]
