Let triangle DEF be equilateral, where the side length is 3. A point G is chosen at random inside the triangle. Find the probability that the length DG is at most 1.
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Let triangle DEF be equilateral, where the side length is 3.
A point G is chosen at random inside the triangle.
Find the probability that the length DG is at most 1.
Draw an equilateral triangle DEF, side 3.
Draw a circle, center at D, 1 inch radius.
Probability = area of circle sector inside triangle / area of triangle not in circle sector
Area of entire circle = (3.1416) • 12 = 3.1416
Area of sector inside triangle = (60 / 360) • 3.1416 = 0.5236
Area of entire triangle = [ sqrt(3) / 4 ] • 32 = 3.8971
Area of triangle outside sector = 3.8971 – 0.5236 = 3.3735
Probability = 0.5236 / 3.3735 = 0.1552 as a percent = 15.52%
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