Question

Please help me solve this problem with work

Answer 1

Answer:

  m∠B ≈ 51.5°

Step-by-step explanation:

A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.

Length BC

The Law of Cosines tells us ...

  a² = b² +c² -2bc·cos(A)

  a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529

  a ≈ 24.8903

Angle B

The Law of Sines tells us ...

  sin(B)/b = sin(A)/a

  B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)

  B ≈ 57.519°

The measure of angle B is about 57.5°.