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Lorico [155]
2 years ago
10

A 16.0-inch chord is drawn in a circle whose radius is 10.0 inches. what is the angular size of the minor arc of this chord? wha

t is the length of the arc, to the nearest tenth of an inch?
Mathematics
1 answer:
statuscvo [17]2 years ago
8 0
PART I
Angular size of the minor arc . 
Half of the chord an the radius makes a right angled triangle with the radius as the hypotenuse and half of the chord as one of the shorter side.
Therefore, using trigonometric ratio, sine = opp/hyp
                          sine θ = 8/10  where θ is half the minor angle
                                  θ  = 53.13
Therefore, the angular size of the minor arc will be 53.13 × 2  = 106.26°

PART II
The length of an arc is given by (θ/360 )× 2πr
where θ is the angle subtended by the arc to the center of the circle and r is the radius of the circle.
Therefore, length = (106.26/360) × 3.142 × 2×10
                            = 18.548 Inches
                                   
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