Answer:
The radius is 18 cm
Step-by-step explanation:
Given that a right triangle △ABC with right angle C is inscribed in a circle.
Also, AC = 18 cm, m∠B = 30°
we have to find the radius of this circle.
In ΔABC
[tex]\sinB=\frac{AC}{AB}=\frac{18}{AB}[/tex]
[tex]AB=\frac{18}{\sin 30}=\frac{18}{\frac{1}{2}}=36cm[/tex]
As given right angle i.e angle C is of 90° which is angle formed in the semicircle. Hence, the hypotenuse side must be the diameter of circle.
Diameter=36 cm
[tex]Radius=\frac{1}{2}\times diameter=\frac{1}{2}\times 36=18 cm[/tex]
