Take several process of thin spaghetti and break them into three lengths each of

Question

Take several process of thin spaghetti and break them into three lengths each of 1 inch, 2 inches, 3 inches, 4 inches, 5 inches, and 6 inches. Discard the extra pieces. Roll three number cubes, and match the number on the cubes, and match the number on the cubes with the lengths of spaghetti. Record the lengths of three sides and whether it is possible to make a triangle with those three lengths. Determine the probability that: (a) no triangle is formed (include the list). (b) An obtuse triangle is formed (include the list). (c) A right triangle is formed (include the list). (d) An acute triangle is formed (include the list). To complete the project, you need to give a complete list of all possible lengths of sides that correspond to the three numbers that appear when you roll the three dice. You may work on the project in pairs or individually. The following definitions may help: 1. The sum of any two sides of a triangle is greater than the third side. 2. An obtuse triangle is a triangle that has one angle measuring greater than 90 degrees. 3. A right triangle is a triangle with one right angle or 90 -degree angle. 4. An acute triangle is a triangle all of whose angles measure less than 90 degrees. For a right triangle, a^2 + b^2 = c^3; for an obtuse triangle, a^2 + b^2 c^2

Explanation / Answer

Total number of combinations = 6C3 = 20

a) P(no triangle is formed) = 13/20

Cases {(1,2,3) (1,2,4) (1,2,5) (1,2,6) (1,3,4) (1,3,5) (1,3,6) (1,4,5) (1,4,6) (1,5,6) (2,3,5) (2,3,6) (2,4,6)}

b) P(obtuse triangle) = 5/20 = 1/4

Cases = {(2,3,4) (2,4,5) (2,5,6) (3,4,6) (3,5,6)}

c) P(right triangle) = 1/20

Case = {(3,4,5)}

d) (acute triangle) = 1/20

Cases = {(4,5,6)}

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.