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 2

Guest Oct 22, 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 2*

Draw DEF, equilateral triangle with side length 3.

Put the point of your compass on D and draw a circle with radius 2.

If DG is within the segment of the circle that's inside the triangle, it will be 2 or less.

If DG is outside the segment of the circle that's inside the triangle, it will be more than 2.

Figure the area of the segment inside the triangle. A_{Segment} I got 2**.**09 (I called it 60/360 of the whole circle.)

Figure the area of the entire triangle. A_{Triangle } I got 3**.**90 (I used sin(60^{o}) to calculate the altitude.)

Divide A_{Segment} by A_{Triangle}. The quotient is the probability. 2**.**09 / 3**.**90 = **0.54**

Guest Oct 23, 2022