Answer:
1.83
Step-by-step explanation:
To find the angle that is subtended at the centre of the circle by the arc, first find the exact radius of the circle, then use the arc length formula to find the measure of the angle.
The formula for the area of a circle is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a circle}}\\\\A=\pi r^2\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$A$ is the area.}\\ \phantom{ww}\bullet\; \textsf{$r$ is the radius.}\end{array}}[/tex]
Given that the area of the circle is 60 cm², its radius can be determined by substituting A = 60 into the area formula and solving for r:
[tex]\pi r^2=60\\\\\\r^2=\dfrac{60}{\pi}\\\\\\r=\sqrt{\dfrac{60}{\pi}}[/tex]
The formula for the arc length of a circle is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Arc length}}\\\\s=r \theta\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$s$ is the arc length.}\\ \phantom{ww}\bullet\; \textsf{$r$ is the radius.}\\ \phantom{ww}\bullet\;\textsf{$\theta$ is the angle measured in radians.}\end{array}}[/tex]
Given that the arc length is 8 cm, substitute s = 8 into the arc length formula, along with the expression for the radius (r), and solve for θ:
[tex]8=\sqrt{\dfrac{60}{\pi}} \cdot \theta\\\\\\\theta=\dfrac{8}{\sqrt{\dfrac{60}{\pi}}}\\\\\\\theta=1.8305824657275...\\\\\\\theta=1.83\; \sf (2\;d.p.)[/tex]
Therefore, the angle that is subtended at the centre of the circle by the arc measured in radians is 1.83 (rounded to two decimal places).
