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In circle G with m∠FGH=46 and FG=16 units, find the length of arc, F, H. Round to the nearest hundredth.

Sagot :

Answer:

12.85

Step-by-step explanation:

Arc Length

Arc length is the distance between two points on a circle's circumference. It's also considered the "edge" of a sector.

There's a formula that calculates the arc length in terms of the circle's radius and, the angle of the sector that the arc length correlates with.

                                                 [tex]s=r\theta[/tex],

where theta is in radians.

Solving the Problem

An image can be drawn to visualize the problem given, see the attached photo below.

Since the length from the circumference or point F, to the center or point G is the radius, r = 16.

The arc FH correlates to the sector FGH, where its angle is 46 degrees. To convert the angle into radians we can simplify use the ratio of degrees to radians or [tex]\dfrac{180}{\pi}[/tex] to find the radian equivalent of 46 degrees.

                                                  [tex]\dfrac{180}{\pi} =\dfrac{46}{x}[/tex]

                                                 [tex]180x=46\pi[/tex]

                                                   [tex]x=\dfrac{46\pi}{180}[/tex]

So, [tex]\theta=\dfrac{46\pi}{180}[/tex].

Plugging in all the known terms, the value of the arc length FH is,

                                        [tex]s=(16)(\dfrac{46\pi}{180})=12.85[/tex].

View image Zarahaider4211
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