Final answer:
Kiera traveled a total of 12.4 meters during her ballet performance, calculated by summing up the distances of each of her movements on stage.
Step-by-step explanation:
To calculate the total distance Kiera traveled during her ballet performance, we need to consider the three separate movements she makes on stage. First, Kiera twirls to Anne's position, which is 5 meters to her left. Then, she leaps to Pete's position, who is 2 meters in front of her original position, but we must calculate the diagonal distance she covers in her leap. Finally, she walks back to her original position, which is 2 meters from Pete.
To calculate the diagonal distance from Anne to Pete, we use the Pythagorean theorem as we are dealing with a right triangle where Anne's position and Kiera's original position are the two legs, and the leap from Anne to Pete is the hypotenuse. The diagonal distance (hypotenuse) is therefore the square root of (2 meters2 + 5 meters2), which equals the square root of (4 + 25) that is, the square root of 29 meters. This approximates to 5.4 meters.
Combining all three distances:
- Twirl to Anne: 5 meters
- Leap to Pete: 5.4 meters
- Walk back to original position: 2 meters
The total distance Kiera travels is 5 + 5.4 + 2, which sums up to
12.4 meters