Let DEF be an equilateral triangle with side length 3. At random, a point G is chosen inside the triangle. Compute the probability that the length DG is less than or equal to 1.
Let DEF be an equilateral triangle with side length 3. At random, a point G is chosen inside the triangle. Compute the probability that the length DG is less than or equal to 1.
Draw equilateral triangle DEF with side length 3.
Place the point of a compass on D and draw a circle with radius 1.
Any point inside the piece of the triangle that's set off by the circle's arc will be 1 or less from D.
Your probability is the area of the piece set off by the arc divided by the area of the entire triangle.
Figure the area of the circle, π r2
then take a sixth of it for the area of the segment. (60/360) • 3.14 • 12
Figure the area of the triangle, (1/2) bh.
You can get the height with Pythagoras' Theorem. h = sqrt(32 – 1.52)
My answer: (0.524 / 3.897) = 0.135 or as a percentage 13.5% probability
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