In circle G with m, angle, F, G, H, equals, 46, degreesm∠FGH=46
∘
and F, G, equals, 16FG=16 units, find the length of arc, F, H
FH
⌢
. Round to the nearest hundredth.
To find the length of arc FH, we can use the formula:
arc length = (central angle / 360) x circumference
First, let's find the circumference of the circle. We know that the radius FG is 16 units, so the diameter FH is double that, which is 32 units. The formula for the circumference of a circle is:
circumference = π x diameter
Substituting the values:
circumference = π x 32
≈ 100.53 units (rounded to the nearest hundredth)
Next, we need to find the central angle FGH. We are given that the measure of ∠FGH is 46 degrees. Since FG is a radius of the circle, and GH is a chord of the circle, we can use the inscribed angle theorem to determine that the measure of the central angle FGH is twice the measure of ∠FGH.
So, m∠FGH = 2 x 46 = 92 degrees.
Now we can use the formula to find the length of arc FH:
arc length = (central angle / 360) x circumference
arc length = (92 / 360) x 100.53
arc length ≈ 25.65 units (rounded to the nearest hundredth)
Therefore, the length of arc FH is approximately 25.65 units.