Respuesta :
Answer: The required length of the diameter of the circumscribed circle is 24 units.
Step-by-step explanation: Given that one side of a triangle has length 12 units and its opposite angle measures 30 degrees.
We are to find the diameter of the circumscribed circle.
We know that
if a, b, c are the lengths of the three sides of a triangle and A, B, C are the corresponding measures of the opposite angles respectively, then the ratio
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}=d,[/tex]
is said to the length of the diameter of the circumscribed circle of the triangle.
According to the given information, we have
a = 12 and A = 30°.
Therefore, the length of the diameter of the circumscribed circle is
[tex]d=\dfrac{a}{\sin A}=\dfrac{12}{\sin 30^\circ}=\dfrac{12}{\frac{1}{2}}=24.[/tex]
Thus, the required length of the diameter of the circumscribed circle is 24 units.
