Respuesta :

Answer:

The length of arc PQ to the nearest tenth is 8.1 inches.

Step-by-step explanation:

Let the measure of arc PQ be 'x'.

Given:

The measure of arc SR = 150°

The measure of arc QR = 65°

The measure of arc PS = 73°

Radius of the circle is, [tex]R=6.48\ in[/tex]

Sum of the measures of all arcs in a circle is always 360°. Therefore,

Arc PQ + Arc QR + Arc SR + Arc PS = 360°

[tex]x+65+150+73=360\\x+288=360\\x=360-288=72\°[/tex]

Now, the arc length is given as:

[tex]\textrm{Arc length}=R\theta\\Where\ \theta\rightarrow arc\ measure\ in\ radians[/tex]

Now, measure of arc PQ, [tex]\theta=72\°=72\times \frac{\pi}{180}=0.4\pi[/tex]

Therefore, arc length PQ = [tex]6.48\times 0.4\pi=2.592\times 3.14=8.138\approx 8.1\ in[/tex]

So, the length of arc PQ to the nearest tenth is 8.1 inches.

Answer : The length of arc PQ is, 8.1 in.

Step-by-step explanation :

First we have to calculate the ∠POQ.

As we know that a circle makes an angle of 360° at center.

That means,

∠POQ + ∠QOR + ∠ROS + ∠SOP = 360°

Given:

∠QOR = 65°

∠ROS = 150°

∠SOP = 73°

∠POQ + 65° + 150° + 73° = 360°

∠POQ + 288° = 360°

∠POQ = 360° - 288°

∠POQ = 72°

Now we have to calculate the length of arc PQ.

Formula used :

Length of arc PQ = [tex]\frac{\theta}{360^o}\times 2\pi r[/tex]

where,

[tex]\theta=72^o[/tex]

r = radius of circle = 6.48 in

Length of arc PQ = [tex]\frac{72^o}{360^o}\times 2\times 3.14\times 6.48in[/tex]

Length of arc PQ = 8.1 in

Therefore, the length of arc PQ is, 8.1 in.

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