Preston is attending a school orchestra concert. He sees his math teacher seated 6.8 feet
ahead of him and his science teacher seated 7.3 feet to his right. How far apart are the two
teachers? If necessary, round to the nearest tenth.
Preston is attending a school orchestra concert. He sees his math teacher seated 6.8 feet ahead of him and his science teacher seated 7.3 feet to his right. How far apart are the two
teachers? If necessary, round to the nearest tenth.
We can use the Pythagorean Theorem to solve this problem. Let's label the distance between Preston and his math teacher as "a" and the distance between Preston and his science teacher as "b". The distance between the math and science teachers can then be labeled as "c", which is what we are trying to find:
a = 6.8 feet
b = 7.3 feet
c^2 = a^2 + b^2
c^2 = (6.8 feet)^2 + (7.3 feet)^2
c^2 = 46.24 feet^2 + 53.29 feet^2
c^2 = 99.53 feet^2
c ≈ sqrt(99.53) feet ≈ 9.98 feet
Therefore, the distance between the math and science teachers is approximately 9.98 feet. Rounded to the nearest tenth, the answer is 10.0 feet.
To find the distance between the two teachers, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance between Preston and his math teacher forms the hypotenuse of a right triangle, and the distance between Preston and his science teacher forms one of the other two sides. The distance between Preston and his math teacher (6.8 feet) will be one side of the right triangle (let's call it side A), and the distance between Preston and his science teacher (7.3 feet) will be the other side (let's call it side B).
We can calculate the distance between the two teachers (the hypotenuse, let's call it C) using the Pythagorean theorem equation: C^2 = A^2 + B^2.
Plug in the given values:
C^2 = 6.8^2 + 7.3^2
Simplify:
C^2 = 46.24 + 53.29
C^2 = 99.53
Now, take the square root of both sides to solve for C:
C = √99.53
Round the answer to the nearest tenth:
C ≈ 9.97
Therefore, the distance between Preston's math teacher and science teacher is approximately 9.97 feet.
To find the distance between the two teachers, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance between the two teachers forms a right triangle, with one side being the distance from Preston to his math teacher and the other side being the distance from Preston to his science teacher.
Let's call the distance between Preston and his math teacher "a" and the distance between Preston and his science teacher "b". We need to find the length of the hypotenuse, which is the distance between the two teachers.
Using the Pythagorean theorem, we have the following equation: a^2 + b^2 = c^2
Substituting the given values, we have (6.8)^2 + (7.3)^2 = c^2
Calculating this, we get 46.24 + 53.29 = c^2
Adding those values, we get 99.53 = c^2
Finally, we can take the square root of both sides to find c, the distance between the two teachers:
c = √99.53 ≈ 9.98 feet.
So, the two teachers are approximately 9.98 feet apart.