Question

Helllppppp Asapppp.

Answer 1

34.77°

Explanation:

In a triangle with sides a, b, and c, the law of cosines tells us that
`c^2=a^2+b^2-2abcos(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+121-308cos(B)\\64=317-308cos(B)\\-253=-308cos(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.