In the triangle, angle B is 48 degrees and angle A is 19 degrees. If side c has a length of 15 cm, use the Law of Sines to find the length of side b. Round your answer to the nearest centimeter.

Question

In the triangle, angle B is 48 degrees and angle A is 19 degrees. If side c has a length of 15 cm, use the Law of Sines to find the length of side b. Round your answer to the nearest centimeter.

Answer 1

First, we need to find the measure of angle C. Since the sum of the angles in a triangle is always 180 degrees, we have:

Angle C = 180 - (48 + 19) = 113 degrees

Now, we can use the Law of Sines to find the length of side b:

sin A / a = sin B / b = sin C / c

sin 19 / b = sin 48 / 15

b = 15 * sin 19 / sin 48
b ≈ 7.84

So, the length of side b is approximately 8 cm.