∆TRI is inscribed in circle P whose diameter is 24 inches, and m∠I
= 60°.
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Find RT, in inches. Round to the nearest hundredth, if necessary.
First, we need to find the radius of circle P, which is half the diameter:
Radius = 24 inches / 2 = 12 inches
Next, we notice that triangle TRI is an equilateral triangle because angle I is 60 degrees.
In an equilateral triangle, all sides are equal. So in this case, RT = TI = RI.
Now, we can use trigonometry to find the length of RT. Since angle I is 60 degrees, we can split triangle TRI into two 30-60-90 right triangles.
In a 30-60-90 right triangle, the side opposite the 30 degree angle is half the length of the hypotenuse. So in our case, RT = RI = TI = 12 * √3 = 20.78 inches.
Therefore, RT is approximately 20.78 inches.