Concept explainers
To enter the program and run it for several times for large values of D like
Explanation of Solution
Given:
Break a stick into three pieces to get the probability that you can join the pieces end-to-end to form a triangle. If the sum of the length of any two pieces is less than or equal to that of the third, a triangle can’t be form. This is known as Triangle Inequality. By an experiment your class can estimate the probability that three pieces of broken stick will form a triangle.
Calculation:
Let D, N, I, X, Y, R, S and T variables used in program. Where D stands for number of sticks you have to break, N stands for first end of stick that is 0, I stands for variable of for loop assign from 1 to D, X and Y are stand for the length of points distance from initial point that is 0, R assigned as X, S assigned as Y − R and T assigned for 1 − R − S. Consider the program below
Program:
'Print this statement "SIMULATION-BREAKING STICKS TO MAKE TRIANGLES" on output screen.
10 PRINT "SIMULATION-BREAKING STICKS TO MAKE TRIANGLES"
'PRINT use to create blank line.
20 PRINT
30 PRINT "HOW MANY STICKS DO YOU WANT TO BREAK”;
40 INPUT D
50 LET N=0
60 FOR I=1 to D
70 LET X=RND(1)
80 LET Y=RND(1)
90 IF X>=Y THEN 70
100 LET R=X
110 LET S=Y.R
120 LET T=1.R.S
130 IF R+S<=THEN 170
140 IF S+T<=R THEN 170
150 IF R+T<=S THEN 170
160 LET N=N+1
170 NEXT I
180 LET P =N/D
190 PRINT
200 PRINT “THE EXPERIMENTAL PROBABILITY THAT”
210 PRINT “A BROKEN STICK CAN FORM A TRIANGLE IS”, P
220 END
Sample Output:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
HOW MANY STICKS DO YOU WANT TO BREAK ?100
THE EXPERIMENTAL PROBABILITY THAT
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.28
Output Explanation:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
Enter number of sticks as 100 which you want to break that is value of variable D
HOW MANY STICKS DO YOU WANT TO BREAK ?100
THE EXPERIMENTAL PROBABILITY THAT
Than you get experimental probability is equal to 0.28
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.28
The probability is less than
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
HOW MANY STICKS DO YOU WANT TO BREAK ?400
THE EXPERIMENTAL PROBABILITY THAT
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.2275
Output Explanation:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
Enter number of sticks as 400 which you want to break that is value of variable D
HOW MANY STICKS DO YOU WANT TO BREAK ?400
THE EXPERIMENTAL PROBABILITY THAT
Than you get experimental probability is equal to 0.2275
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.2275
The probability is less than
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
HOW MANY STICKS DO YOU WANT TO BREAK ?800
THE EXPERIMENTAL PROBABILITY THAT
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.26375
Output Explanation:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
Enter number of sticks as 800 which you want to break that is value of variable D
HOW MANY STICKS DO YOU WANT TO BREAK ?800
THE EXPERIMENTAL PROBABILITY THAT
Than you get experimental probability is equal to 0.26375
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.26375
The probability is less than
Chapter 6 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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