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 74.8 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 93.5 ft from the trumpet player. How far did the tuba player march?
-----In the picture it formed a triangle. I think its a pythagorean thereom problem but its not coming out correctly. I put 74.8 and 93.5 as the legs. PLEASE HELP!!!
if you labeled the legs as you say, you are assuming that the tuba player marched 93.5 feet toward the sideline.
Bzzzt, but thanks for playing.
Label the hypotenuse 93.5 and I think you will get better results.
Pos it.
To solve this problem, you can indeed 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, we can consider the trumpet player's march as one leg of the triangle, the tuba player's march as the other leg, and the distance between them as the hypotenuse.
Let's call the distance the tuba player marched "x". According to the problem, the trumpet player marched 74.8 ft. Therefore, we have a right triangle with legs measuring 74.8 ft and x ft, and a hypotenuse measuring 93.5 ft.
Using the Pythagorean theorem, we can write:
(leg1)^2 + (leg2)^2 = (hypotenuse)^2
Substituting the given values:
(74.8)^2 + (x)^2 = (93.5)^2
Now we can solve for x:
(74.8)^2 + (x)^2 = (93.5)^2
5565.04 + (x)^2 = 8722.25
(x)^2 = 8722.25 - 5565.04
(x)^2 = 3157.21
x = √(3157.21)
x ≈ 56.16 ft (rounded to two decimal places)
Therefore, the tuba player marched approximately 56.16 ft.
Note: If you were not getting the correct answer, please double-check your calculations to ensure you used the correct values and performed the required operations accurately.