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.
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
1 answer