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If YV = 28 in, find the length of the major arc VYX. Round to the nearest tenth ( one decimal place).

Sagot :

MrRoyal

Answer:

[tex]VYX=84.3in[/tex]

Step-by-step explanation:

Given

[tex]YV = 28in[/tex]

[tex]\angle WZX = 15^\circ[/tex]

See attachment

Required

Determine the length of [tex]VYX[/tex]

First, calculate the major angle VZX

[tex]\theta = \angle VZX = 360 - \angle WZX[/tex]

[tex]\theta = \angle VZX = 360 - 15[/tex]

[tex]\theta = \angle VZX = 345[/tex]

[tex]\theta = 345[/tex]

The length of arc VYX, is:

[tex]L=\frac{\theta}{360} * 2\pi r[/tex]

Where

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]r = \frac{1}{2} * YV[/tex]

[tex]r = \frac{1}{2} * 28[/tex]

[tex]r = 14[/tex]

So:

[tex]L=\frac{\theta}{360} * 2\pi r[/tex]

[tex]L=\frac{345}{360} * 2 * \frac{22}{7} *14[/tex]

[tex]L=\frac{345}{360} * 2 * 22 *2[/tex]

[tex]L=\frac{345* 2 * 22 *2}{360}[/tex]

[tex]L=\frac{30360}{360}[/tex]

[tex]L=84.3in[/tex]

Hence, the length of VYX is:

[tex]VYX=84.3in[/tex]

View image MrRoyal
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