The three panels are divided into three equal parts. This mean that the central angle from each panel is 120 degrees. So, the side length of w and the length of curve xy is 7 feet and 8 feet
Let the center of the circle be O (see attachment).
So:
[tex]\angle XOY = \frac{360}{3} = 120^o[/tex] ---- because the circle is divided into 3 equal parts
Considering [tex]\triangle XOY[/tex]
[tex]\angle W O Y = \frac{\angle X O Y}{2}[/tex]
[tex]\angle WOY = \frac{120}{2} = 60[/tex]
Considering [tex]\triangle WOY[/tex]
[tex]\sin(60) = \frac{wy}{yo}[/tex]
Where:
[tex]yo= 4[/tex]
So, we have:
[tex]\sin(60) = \frac{wy}{4}[/tex]
[tex]0.8860 = \frac{wy}{4}[/tex]
Multiply through by 4
[tex]wy = 4 * 0.8660[/tex]
[tex]wy = 3.464[/tex]
Because w divides xy into w equal parts
[tex]wx = wy = 3.464[/tex]
The length of w is:
[tex]w =wx + wz[/tex]
[tex]w = 3.464+3.464[/tex]
[tex]w = 6.928[/tex]
Approximate
[tex]w = 7[/tex]
Next, is to calculate arc length xy
This is calculated as follows:
[tex]xy = \frac{\theta}{360} * 2\pi r[/tex]
Where:
[tex]\theta = \XOY = 120^o[/tex]--- central angle
So, we have:
[tex]xy = \frac{\theta}{360} * 2\pi r[/tex]
[tex]xy = \frac{120}{360} * 2 * 3.142 * 4[/tex]
[tex]xy = \frac{1}{3} * 25.136[/tex]
[tex]xy = 8.33[/tex]
Approximate
[tex]xy = 8[/tex]
Hence, the side length of w and the length of curve xy is 7 feet and 8 feet respectively.
Read more about solving triangles at:
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