Question

Mrs. Harper is teaching a 5th grade class. She is

standing 6 meters in front of Annie. Javier is
sitting to Annie's right. If Javier and Mrs. Harper
are 8 meters apart, how far apart are Annie and
Javier? If necessary, round to the nearest tenth.

This is a Pythagorean theorem word problem

Answer 1

Annie and Javier are 10 meters apart.

Explanation:

We can use the Pythagorean theorem to solve this problem. Let's call the distance between Annie and Javier "x". Then, we have two right triangles:

The first right triangle is formed by Mrs. Harper, Annie, and the distance between Mrs. Harper and Annie. We know that Mrs. Harper is 6 meters in front of Annie, so the hypotenuse of this triangle is 6 meters.

The second right triangle is formed by Mrs. Harper, Javier, and the distance between Mrs. Harper and Javier. We know that Mrs. Harper and Javier are 8 meters apart, so the hypotenuse of this triangle is 8 meters.

Since Mrs. Harper is the common point of both triangles, we can combine them to form a larger right triangle with sides of 6 meters, 8 meters, and x meters:

Using the Pythagorean theorem, we have:

6^2 + 8^2 = x^2

Simplifying:

36 + 64 = x^2

100 = x^2

Taking the square root of both sides:

x = 10

Therefore, Annie and Javier are 10 meters apart.