Answer:
r = 29
Step-by-step explanation:
We assume your diagram is showing ...
To find r, use the relationship between the side lengths of the triangle.
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In a 30°-60°-90° triangle, the ratio of shortest to longest sides is 1 : 2. Therefore, we have ...
CD/CA = r/(r+29) = 1/2
2r = r +29 . . . . . . multiply by 2(r+29)
r = 29 . . . . . . . . . .subtract r
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The knowledge of 30°-60°-90° triangle relationships can come from any of several sources. One such source is consideration of what happens when you cut an equilateral triangle along its altitude. (The short side is half the long side of the resulting 30-60-90 triangle.)
Another source is the sine ratio of the 30° angle (trigonometry). Sin(30°) = CD/CA = 1/2.
