We have been given that a right △ABC is inscribed in circle k(O, r).
m∠C = 90°, AC = 18 cm, m∠B = 30°. We are asked to find the radius of the circle.
First of all, we will draw a diagram that represent the given scenario.
We can see from the attached file that AB is diameter of circle O and it a hypotenuse of triangle ABC.
We will use sine to find side AB.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(30^{\circ})=\frac{AC}{AB}[/tex]
[tex]\text{sin}(30^{\circ})=\frac{18}{AB}[/tex]
[tex]AB=\frac{18}{\text{sin}(30^{\circ})}[/tex]
[tex]AB=\frac{18}{0.5}[/tex]
[tex]AB=36[/tex]
Wee know that radius is half the diameter, so radius of given circle would be half of the 36 that is [tex]\frac{36}{2}=18[/tex].
Therefore, the radius of given circle would be 18 cm.
