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
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.