Answer:
7.5 Units
Step-by-step explanation:
Angle ABC of triangle ABC is a Right angle. The sides of ABC are the diameters of semicircles
The area of the semicircle on AB equals 8pi
Area of a semicircle[tex]=\frac{\pi r^2}{2}[/tex]
Therefore:
[tex]\frac{\pi r^2}{2}=8\pi\\r^2=16\\r=4[/tex]
Next, the arc of the semicircle on AC has length 8.5pi.
Length of arc of a semicircle =[tex]\pi r[/tex]
[tex]\pi r=8.5\pi\\r=8.5[/tex]
Using Pythagoras theorem
[tex]8.5^2=4^2+x^2\\x^2=8.5^2-4^2\\x^2=56.25\\x=\sqrt{56.25} \\x=7.5[/tex]
Radius of the semicircle of BC=7.5 Units
