Answer:
The radius of the circle is:
[tex]3~\text{cm}[/tex]
Step-by-step explanation:
OB is the radius, and AB is a tangent.
When a radius and tangent touch, the angle formed between them is a right angle.
So, we can say that:
[tex]\angle{OBA}=90^{\circ}[/tex]
Making OAB a right triangle.
We have [tex]OA=6[/tex], with it being the hypotenuse of the triangle.
We also have the angle: [tex]30^{\circ}[/tex]
Which makes our missing side (the radius) to be the opposite side to the angle. Let's take it to be [tex]x[/tex].
The sine trigonometric ratio is the one we will make use of here:
[tex]\sin{\theta}=\frac{O}{H}[/tex]
Where O is the opposite side, and H is the hypotenuse.
Substitute the values into the equation:
[tex]\sin{30^{\circ}}=\frac{x}{6}[/tex]
Find the value of x:
[tex]\sin{30^{\circ}\times 6=\frac{x}{6}\times 6\\\\\sin{30^{\circ}\times 6=x\\x=3[/tex]
So, the radius of the circle is:
[tex]3~\text{cm}[/tex]
