Answer:
34.77°
Step-by-step explanation:
In a triangle with sides a, b, and c, the law of cosines tells us that[tex]c^2=a^2+b^2-2ab\cos{C}[/tex], where C is the angle between sides a and b and across from side c. On this triangle, we can say a = 14, b = 11, c = 8, and C = m∠B; plugging these values in, we have
[tex]8^2=14^2+11^2-2(14)(11)\cos{B}\\[/tex]
Simplifying this equation:
[tex]64=196+121-308\cos{B}\\64=317-308\cos{B}\\-253=-308\cos{B}\\253/308=\cos{B}[/tex]
to unwrap this, we can put each side through the inverse cosine function:
[tex]\cos^{-1}{(253/308)}\cos^{-1}{(\cos{B})}\\34.77^{\circ}\approx B[/tex]
And we have our result for m∠B.
