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 .
405 mm
3,835 mm
385 mm
366 mm
To use the Law of Sines, we first need to identify the values of an angle and its opposite side. In this case, we know ∠A is 72 degrees and side a is 1,246 mm.
The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant in any triangle.
We can set up the proportion:
a/sin(A) = c/sin(C)
Plugging in the given values, we have:
1,246/sin(72) = c/sin(C)
Using the law of Sines, we can find C:
sin(C) = (c * sin(A)) / a
sin(C) = (c * sin(72)) / 1,246
sin(C) = (c * 0.9510) / 1,246
To solve for C, we need to take the inverse sine (sin^(-1)) of both sides:
C = sin^(-1)((c * 0.9510) / 1,246)
Since the sum of angles in a triangle is 180 degrees, we can find C by subtracting 72 degrees from 180 degrees:
C = 180 - 72
C = 108 degrees
Now we can substitute the value of C back into our equation:
1,246/sin(72) = c/sin(108)
To solve for c, we can cross multiply:
(c * sin(72)) = (1,246 * sin(108))
Dividing both sides by sin(72):
c = (1,246 * sin(108)) / sin(72)
c ≈ 3835 mm
So, using the Law of Sines, the length of side c is approximately 3,835 mm.