The quarterback throws a pass from 10 yards from a goal line and 25 yards from a sideline. A receiver catches the pass at 40 yards from the same goal line and 5 yards from the same sideline. How long was the pass?
This is a right-angle triangle and you need to find the hypotenuse.
Pythagorean Theorem:
a^2 + b^2 = c^2
30^2 + 20^2 = c^2
900 + 400 = c^2
1300 = c^2
36.06 yards = c
in a football game a quarterback throws a pass is caught on 15 yards line 10 yards from the side line the pass is caught on the 40 yard line 45 yards from the same sideline how long was the pass
To find the length of the pass, 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 from the quarterback to the receiver represents the hypotenuse of a right triangle. The distance from the goal line to the receiver's catching point represents one side of the triangle, and the distance from the sideline to the catching point represents the other side.
Let's calculate the length of the pass using the Pythagorean theorem:
Distance from the goal line to the catching point: 40 yards
Distance from the sideline to the catching point: 5 yards
Using the Pythagorean theorem:
Length of the pass = sqrt((Distance from the goal line to the catching point)^2 + (Distance from the sideline to the catching point)^2)
Length of the pass = sqrt((40 yards)^2 + (5 yards)^2)
Length of the pass = sqrt(1600 yards^2 + 25 yards^2)
Length of the pass = sqrt(1625 yards^2)
Calculating the square root:
Length of the pass ≈ 40.31 yards
Therefore, the length of the pass is approximately 40.31 yards.
To determine the length of the pass, we can use the Pythagorean theorem. This 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 quarterback's starting position can be considered as one point of the right triangle, the receiver's catching position as another point, and the length of the pass as the hypotenuse.
Let's label the starting point of the quarterback as point A (10 yards from the goal line and 25 yards from the sideline), the catching point of the receiver as point B (40 yards from the goal line and 5 yards from the sideline), and the length of the pass as c.
Using the Pythagorean theorem, we can write the equation:
c^2 = (40 - 10)^2 + (5 - 25)^2
Simplifying the equation:
c^2 = 30^2 + (-20)^2
c^2 = 900 + 400
c^2 = 1300
Taking the square root of both sides to isolate c:
c = √1300
Calculating the square root:
c ≈ 36.06 yards
Therefore, the length of the pass is approximately 36.06 yards.