During the half-time show of a football game, a trumpet player and a tuba player start at the same position on the field. The trumpet player then marches 76.4 ft directly toward the goal line, and the tuba player marches directly toward the sideline. At the end of their march, the tuba player is 95.5 ft from the trumpet player. How far did the tuba player march?

Question

During the half-time show of a football game, a trumpet player and a tuba player start at the same position on the field. The trumpet player then marches 76.4 ft directly toward the goal line, and the tuba player marches directly toward the sideline. At the end of their march, the tuba player is 95.5 ft from the trumpet player. How far did the tuba player march?

Answer 1

This sounds like a right triangle.

a^2 + b^2 = c^2

76.4^2 + b^2 = 95.5^2

5836.96 + b^2 = 9120.25

b^2 = 3283.29

b = 57.3 feet

Answer 2

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square 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, let's call the distance the tuba player marches "x" ft.

According to the problem, the trumpet player marches 76.4 ft directly toward the goal line, so the distance between them is the hypotenuse of a right triangle. The other two sides of the triangle are the distance the tuba player marches (x ft) and the distance the tuba player is from the starting position.

Using the Pythagorean theorem, we can write the equation:

76.4^2 = x^2 + 95.5^2

Now let's solve for x.

76.4^2 = x^2 + 95.5^2
5849.96 = x^2 + 9120.25
x^2 = 5849.96 - 9120.25
x^2 = -3270.29

Since we cannot take the square root of a negative number, it seems there is an error in the problem. Please double-check the given information or provide any additional information if available.

Answer 3

To find how far the tuba player marched, we can use the distance formula.

The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the square 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 the trumpet player and the tuba player forms a right triangle.

Let's label the distance the tuba player marched as "x." Since the trumpet player marched directly toward the goal line, their distance remains the same as given in the question, which is 76.4 feet.

Using the distance formula, we can set up an equation:

x^2 + 76.4^2 = 95.5^2

Simplifying this equation:

x^2 + 5856.96 = 9120.25

Subtracting 5856.96 from both sides gives:

x^2 = 3263.29

To solve for x, we can take the square root of both sides:

x = √3263.29

x ≈ 57.11

Therefore, the tuba player marched approximately 57.11 feet.