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# whats the radius if the arc length is 40cm and the central angle is 20 degrees

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whats the radius if the arc length is 40cm and the central angle is 20 degrees

Guest Feb 24, 2015

#1
+227
+5

Well, this is just plain solving equations. From your problem, s=40 and θ=20°. Never mind, you need to know how to make degrees radians. To do this, just use a proportion:$$\frac{degrees}{radians} = \frac{180}{pi}$$

You have degrees, so just plug stuff in and cross multiply. This gives you 20π=180*(x radians). (x is what we're solving for.) Solving gives x= π/9 radians.

Now we know θ in terms of radians. We can just plug our numbers in and solve!

40=r(π/9)

Divide by π/9 to get r=360/π cm!

EDIT: CPhill pointed out to me that I had made a mistake: 40*9=360, not 540 as I had put earlier.

ThisGuy  Feb 24, 2015
Sort:

#1
+227
+5

Well, this is just plain solving equations. From your problem, s=40 and θ=20°. Never mind, you need to know how to make degrees radians. To do this, just use a proportion:$$\frac{degrees}{radians} = \frac{180}{pi}$$

You have degrees, so just plug stuff in and cross multiply. This gives you 20π=180*(x radians). (x is what we're solving for.) Solving gives x= π/9 radians.

Now we know θ in terms of radians. We can just plug our numbers in and solve!

40=r(π/9)

Divide by π/9 to get r=360/π cm!

EDIT: CPhill pointed out to me that I had made a mistake: 40*9=360, not 540 as I had put earlier.

ThisGuy  Feb 24, 2015

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