Find the angle subtended at the centre of a circle of radius 'a' by an arc of length (a pie/4 ) cm
Angle α (in radians) subtended at the centre of a circle of radius R by an arc of length A is
α = A/R radians
= 180A/πR degrees
Example:
Arc = π/2 m
Radius = 3 m
Angle = (π/2)/3 radian
=π/6 radian
all the way around = 2 pi a
fraction of circumference = (a pi/4) /(2 pi a)
= 1/8
(1/8) 360 = 45 degrees = pi/4 radians
To find the angle subtended at the center of a circle, we can use the formula:
θ = (s / r)
Where θ is the angle in radians, s is the length of the arc, and r is the radius of the circle.
In this case, the length of the arc is (aπ/4) cm, and the radius of the circle is 'a' cm.
Substituting the values into the formula, we have:
θ = ((aπ/4) / a)
Cancel out the 'a' in the numerator and denominator:
θ = (π/4)
Therefore, the angle subtended at the center of the circle is π/4 radians.