Use the Law of Sines to find the missing side of the triangle. Find b.

Solution:

Given the angle A= 58 ; angle B = 48

Given the sides BC =50, AC =b

Here a is side length opposite of angle A

b is side length opposite to angle B

c is side length opposite to angle C

We have law of sines : sinA /a = sinB/b = sinC/c

Consider sinA /a = sinB/b

sin58 /50 = sin48/b

bsin58° = 50 × sin48°

b =(50 × sin48°)/sin58°

b = (50 × 0.74)/0.85

b = 43.5

Use the Law of Sines to find the missing side of the triangle. Find b.

Summary:

By using the Law of Sines to find the missing side of the triangle, we get b value as 43.5 units.