Question

Use the law of sines to solve the triangle. Given: b=48, c=47, ∠C=39^∘

Answer 1

From the given: b=48, c=47, ∠C=39⁰, the lengths of the sides of triangle are approximately a = 58.4403, b = 48, and c = 47.

Step-by-step explanation:

To solve the triangle using the law of sines, we can use the formula:

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

In this case, we are given that b = 48, c = 47, and angle C is 39 degrees. Let's substitute these values into the formula:

a/sin(A) = 48/sin(B) = 47/sin(39)

Now, we can solve for a and sin(A) using the first and second equations:

a = 48(sin(A)/sin(B))

a = 48(sin(39)/sin(B))

Next, we can solve for sin(B) using the third equation:

sin(B) = (47/sin(39))sin(39)

Using a calculator, we find that sin(B) ≈ 0.7577

Substituting this value back into the equation for a:

a ≈ 48(0.7757/sin(B))

Using a calculator, we find that a ≈ 58.4403

Therefore, the lengths of the sides are approximately a = 58.4403, b = 48, and c = 47.