there are three proposed triangular courses for the beginner sailors. The lengths of each leg of the race and the distance from the starting line to the finish line for each proposed course are listed below. Which course would be appropriate for the right triangle regatta? Explain your answer, including reasons for not choosing the other two
To determine which proposed course is appropriate for the right triangle regatta, we need to identify the course that has the appropriate side lengths corresponding to a right triangle.
A right triangle is a triangle that has one angle measuring 90 degrees. In such a triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
Let's review the lengths of each leg and the distance from the starting line to the finish line for each proposed course:
Course 1:
Leg 1: 3 units
Leg 2: 4 units
Distance from starting line to finish line: 5 units
Course 2:
Leg 1: 5 units
Leg 2: 12 units
Distance from starting line to finish line: 13 units
Course 3:
Leg 1: 6 units
Leg 2: 8 units
Distance from starting line to finish line: 9 units
Now, let's apply the Pythagorean theorem to each proposed course to check if any of them form a right triangle:
Course 1:
3^2 + 4^2 = 9 + 16 = 25
5^2 = 25
Course 2:
5^2 + 12^2 = 25 + 144 = 169
13^2 = 169
Course 3:
6^2 + 8^2 = 36 + 64 = 100
10^2 = 100
By applying the Pythagorean theorem, we can see that only Course 1 satisfies the condition of a right triangle. Therefore, Course 1 is appropriate for the right triangle regatta.
Reasons for not choosing the other two courses:
Course 2 and Course 3 have lengths that do not satisfy the Pythagorean theorem for a right triangle. In other words, the sum of the squares of the lengths of the two shorter sides is not equal to the square of the length of the longest side. Therefore, they are not appropriate for the right triangle regatta.