Question

Find the angle, 0 measured in radians, when r=7 and the arc length is 10.5

Answer 1

For the given question ,

The radius r= 7

and length of an arc =10.5

Also ,we know that

length of an arc = θ/360*(2pie *r)

where, θ is the angle and (2*pie*r) is the circumference of the circle.

therefore, 10.5=(θ/360)* 2*pie*7

on further calculations,

θ=85.9 degrees

or θ=86 degrees(approx).

Answer 2

Θ = 1.5 radians

Explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle , then

10.5 = 2πr ×
`(0)/(2\pi )` ( cancel 2π on numerator/ denominator )

10.5 = 7 × Θ ( divide both sides by 7 )

`(10.5)/(7)` = Θ , then

Θ = 1.5 radians