Answer:
The arc length XY is equal to [tex]\frac{50}{9}\pi\ ft[/tex] or [tex]17.4\ ft[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the circumference of the circle H
The circumference is given by the formula
[tex]C=2 \pi r[/tex]
we have
[tex]r=xh=10\ ft[/tex]
substitute
[tex]C=2 \pi (10)\\C=20\pi\ ft[/tex]
step 2
we know that
The circumference of a circle subtends a central angle of 360 degrees
so
using proportion
Find out the length of the arc xy if the central angle is equal to 100 degrees
Remember that
[tex]m\angle XHY=arc\ XY=100^o[/tex] ---> by central angle
[tex]\frac{20\pi}{360^o}=\frac{x}{100^o}\\\\x=20\pi(100)/360\\\\x=\frac{2,000}{360}\pi\ ft[/tex]
Simplify
[tex]x=\frac{50}{9}\pi\ ft[/tex] ----> exact value
To find out the approximate value
assume
[tex]\pi=3.14[/tex]
substitute
[tex]x=\frac{50}{9}(3.14)=17.4\ ft[/tex] ----> approximate value
therefore
The arc length XY is equal to [tex]\frac{50}{9}\pi\ ft[/tex] or [tex]17.4\ ft[/tex]
The arc length is 17.4 feet
The arc length is given as,
[tex]\theta=\frac{arc}{radius}[/tex]
From given figure, It is observed that radius is 10 feet and angle is 100 degree.
Convert 100 degree into radian,
[tex]100degree=100*\frac{\pi}{180} =1.74 radian[/tex]
Substitute values in above relation.
[tex]1.74=\frac{arc}{10}\\ \\arc=1.74*10=17.4feet[/tex]
Thus, the arc length [tex]xy[/tex] is 17.4 feet
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