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# help! probability...

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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.

Nov 15, 2022

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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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Nov 15, 2022