Question

Three ballet dancers are positioned on stage. Kendall is straight behind Bridget and directly left of Lena. If Bridget and Kendall are 5 feet apart, and Lena and Bridget are 7 feet apart, what is the distance between Kendall and Lena? If necessary, round to the nearest tenth.

Answer 1

The distance between Kendall and Lena is approximately 8.6 feet, rounded to the nearest tenth.

Work:

Start by drawing a diagram to visualize the positions of the three ballet dancers. Let's represent Kendall, Bridget, and Lena with the letters K, B, and L, respectively. Based on the given information, we can write:

Kendall is straight behind Bridget and directly left of Lena, so the positions of the dancers are arranged in a straight line as follows:

L --- B --- K

Bridget and Kendall are 5 feet apart, so we can write:

KB = 5 feet

Lena and Bridget are 7 feet apart, so we can write:

BL = 7 feet

To find the distance between Kendall and Lena, we can use the Pythagorean theorem. Let's call the distance between Kendall and Lena "KL". Then we have:

KL^2 = KB^2 + BL^2

KL^2 = 5^2 + 7^2

KL^2 = 74

Taking the square root of both sides, we get:

KL ≈ 8.6 feet

Answer 2

Travis and Shawn form the vertical leg of a right angle triangle of length = 8 ft. Andy and Travis form the hypotenuse of the right angle triangle of length = 9 ft.

Explanation:

Using the Pythagorean theorem to find the distance between Shawn and Andy which is the length of the horizontal leg of the right angle triangle; let that length be x. Then:

92 = 82 + x2 , x2 = 92 - 82 = 81 - 64 = 17 , and x = √ 17 = 4.13 ft