ineedhelponmyhw
If arc AB measures 155°, what is the length of the radius of the circle, to the nearest hundredth? drawing pic now.
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ineedhelponmyhw
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|dw:1342078364411:dw|
Malaria
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Arc Length = Radius * Plane Angle
Angle must be in radians
ineedhelponmyhw
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can you help me out . i dont understand
ineedhelponmyhw
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-.-
Malaria
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Convert your angle to radians first. Do you know the formula for that?
Malaria
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I'm here for you, it's not as bad as it looks.
ineedhelponmyhw
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no thats the problem
Malaria
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Ok, the conversion for degrees to radians is:
\[Angle*\pi/180\]
ineedhelponmyhw
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155*pi/180
?
Malaria
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Correct.
ineedhelponmyhw
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2.705260341
Malaria
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Okay, now solve the Arc Length formula for radius
Malaria
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Solve the initial formula for radius:
Arc Length = radius * angle
ineedhelponmyhw
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486.9468613 = 2.705260341* 180
?
Malaria
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Hold on, I think you're a little confused still.
We know the Arc Length: That was given in your drawing as 14cm
We know the angle (that you converted to radians) as 2.705260341
What we're looking for is the radius of the circle that fits those conditions.
We can use the formula that I have you to find any single piece of the info that we're missing if we're given the other two.
ineedhelponmyhw
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i dont understand this at alll
Malaria
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Let's call the Arc Length S and the Radius R and the Angle A.
So:
S=RA
Divide through by A to get:
S/A = R
So the radius of the circle (R) is equal to the arc length (S) divided by the Angle in radians (A)
ineedhelponmyhw
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can yu do for me?
Malaria
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R = (14)/(2.705260341)
Malaria
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So R = ?
ineedhelponmyhw
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37.87364477
?
Malaria
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When I divide 14 by 2.705260341, I'm getting 5.175.
Rounded to the nearest tenth, that should be 5.2
ineedhelponmyhw
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oh whoops i accidentally mult instead of divide
ineedhelponmyhw
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so the answer is 5.175102665
?
Malaria
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Yes, don't forget to round to the nearest tenth though.