9.2.3 Geometric Probability (continued)
The probability that a randomly chosen point will lie inside the rhombus is equal to the ratio of the area of the rhombus to the area of the large rectangle. To calculate the area of the rhombus, determine the length of the short diagonal as twice the length of the leg of the 30°-60°-90° triangle, or 20 3. m. The length of the longer diagonal is the 10 m-length of the short leg of the small triangle plus the 20 m-length of the hypotenuse of the small triangle all times 2, or 60 m. The area of the rhombus is = = = A d d (1/2) (1/2)(20 3)(60) 600 3 m 1 2 2 . P The probability is 600 3/6000 0.17. = ≈
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