Question

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Answer 1

Answer:

34.77°

Step-by-step explanation:

In a triangle with sides a, b, and c, the law of cosines tells us that$c^2=a^2+b^2-2ab\cos{C}$, 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

$8^2=14^2+11^2-2(14)(11)\cos{B}$

Simplifying this equation:

$64=196+121-308\cos{B}\\64=317-308\cos{B}\\-253=-308\cos{B}\\253/308=\cos{B}$

to unwrap this, we can put each side through the inverse cosine function:

$\cos^{-1}{(253/308)}\cos^{-1}{(\cos{B})}\\34.77^{\circ}\approx B$

And we have our result for m∠B.