Right triangle upper A upper B upper C has a small square box at angle B. The side opposite of each angle is labeled as the lowercase letter of the angle name.
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 .
To find side c using the Law of Sines, we can use the formula:
a/sin(A) = c/sin(C)
Given that ∠A = 72 degrees and a = 1246 mm, we have:
1246/sin(72) = c/sin(180-72-C)
1246/sin(72) = c/sin(108)
Now, we need to find ∠C using the fact that the sum of all angles in a triangle is 180 degrees:
∠A + ∠B + ∠C = 180
72 + 90 + ∠C = 180
162 + ∠C = 180
∠C = 18 degrees
Now, plug this back into the Law of Sines formula:
1246/sin(72) = c/sin(18)
Solving for c:
c = 1246 * sin(18) / sin(72)
c = 1246 * 0.309 / 0.951
c = 405 mm
Therefore, the length of side c is 405 mm.