Question

Use the Law of Sines to find the missing angle of the triangle. Find given that 83, 44, and 31.

Answer 1

See attachment for Answer

Answer 2

∠B = 72.7°.

∠C = 76.3°

Explanation:

The law of sine sinA /a = sinB/b = sinC/c

Let's find angle C.

(sinC)/c = (sinA)/a

C = sin⁻¹(c·sinA / a)

Plugging in numbers:

C = sin⁻¹(83·sin(31) / 44)

= sin⁻¹(0.97155)

Angle C = 76.3°

We know that the sum of the internal angles of a triangle is 180°.

Therefore, B = 180 - (A + C)

= 180 - (31 + 76.3)

= 180 - 107.3

= 72.7°

∠B is 72.7°.

Hope this will helpful.

Thank you.