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Find the length of arc AB, round to the nearest tenth.

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Find the length of arc AB, round to the nearest tenth. 
Circle C with radii CA and CB.  CA = 6.  Central angle BCA = 125 degrees
A. 6.5
B. 8.3
C. 13.1
D. 14.2
 
Find the radius of circle A, if the area of the shaded region is 47.5 cm2
Circle “A” with a central angle cutting an arc of 85 degrees.  The interior of this sector is shaded.
A. 7 cm
B. 7.5 cm
C. 8 cm
D. 8.5 cm
 
How do you find the arc length of a central angle of a circle? 
A. image
B. image
C. image
D. none of the above

 

asked Sep 25, 2014 in TRIGONOMETRY by tonymate Pupil

3 Answers

0 votes
 
Best answer

(1).

Calculate the length of the arc AB by using formula :

L = (C/360) * 2πr, where C = is the central angle of the arc in degrees, r = the radius of the arc.

Substitute C = 125, π = 22/7 ≅ 3.142 and r = 6 in the above formula.

AB = 125/360 * 2 * 22/7 * 6

     = 33000/2520

     ≅ 13.1 units.

The option C is correct.

answered Sep 25, 2014 by casacop Expert
selected Sep 26, 2014 by tonymate
+1 vote

(2).

Calculate the radius of the circle by using the sector area formula :

A = (C/360) * πr2, where C = is the central angle of the arc in degrees, r = the radius of the arc.

Substitute A = 47.5 cm2, C = 85 and π = 22/7 ≅ 3.142 in the above formula.

47.5 = 85/360 * 22/7 * r2

64 r2

r = ± 8.

Radius of the circle cannot be expressed with negative sign.

r = 8 cm.

The option C is correct.

answered Sep 25, 2014 by casacop Expert
edited Sep 25, 2014 by bradely
0 votes

(3).

Calculate the length of the arc by using formula : s = r * θ, where θ = is measured in radians, r = the radius of the circle.

The option C is correct.

 

answered Sep 25, 2014 by casacop Expert

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