Use the Law of Sines to find the length of side c, to the nearest millimeter, if ∠A=72 degrees and side a=1,246 mm . (1 point) Responses 405 mm 405 mm 3,835 mm 3,835 mm 385 mm 385 mm 366 mm

Answer 1

To use the Law of Sines, we can set up the equation:

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

Given that ∠A = 72 degrees and side a = 1,246 mm, we can substitute the values into the equation:

sin(72) / 1,246 = sin(C) / c

To find sin(72), we can use a calculator or reference table.

sin(72) ≈ 0.951

Substituting this value, we have:

0.951 / 1,246 = sin(C) / c

To isolate c, we can cross multiply:

c = (1,246 * sin(C)) / 0.951

Now we need to find sin(C). Since the sum of angles in a triangle is 180 degrees, we know that:

∠C = 180 - ∠A - ∠B

Since ∠A = 72 degrees, we can calculate ∠C:

∠C = 180 - 72 - 180

∠C = 108 degrees

Using a calculator or reference table, we can find sin(108):

sin(108) ≈ 0.944

Substituting this value back into the equation, we have:

c = (1,246 * 0.944) / 0.951

c ≈ 1236 / 0.951

c ≈ 1299 mm

Therefore, the length of side c to the nearest millimeter is 1299 mm.