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Sagot :
The angle that defines the arc is 1.57 radians or 90°.
How to get the angle of the arc?
For a circle of radius R, the length of an arc defined by an angle θ in radians is given by:
L = θ*R.
Here we know that the radius is R = 7cm, and the length of the arc is 10.99 cm. Replacing these in the above equation:
10.99 cm = θ*7cm
θ = (10.99 cm/7 cm) = 1.57
Then the angle is 1.57 radians. Remember that:
3.14 radians = 180°
Then:
θ = (1.57/3.14)*180° = 90°
If you want to learn more about arcs:
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[tex]\\ \rm\Rrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{180\ell}{r\pi}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{180(10.99}{7(3.14)}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{1978.2}{7\pi}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=90^{\circ}[/tex]
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