A preseason game Tennessee Titans punter A.J. Trapasso hit the giant HD TV screen suspended above the field at the new Cowboys stadium. At the time of the punt A.J. was 30 yards away from the edge of the tv screen (the tv screen starts at the 40 yard line, and AJ was at the 10 yard line), and he kicked the ball straight at a 70 degree angle. How high is the video screen ?
82.4 ft high
30tan70
To determine the height of the video screen, we need to use some trigonometry to calculate the vertical distance the ball traveled. Here's how we can do it:
1. Draw a diagram to visualize the situation. Draw a right triangle where the horizontal leg represents the 30 yards from AJ to the edge of the TV screen, the vertical leg represents the height of the screen, and the hypotenuse represents the diagonal distance the ball traveled.
/|
/ |
/ |
/ |
/θ |
/____|
2. Since we know that AJ kicked the ball at a 70-degree angle, label the angle as θ in the diagram.
3. Now, using trigonometry, we can use the sine function to find the vertical distance (height) of the video screen.
The formula for the sine function is: sin(θ) = opposite/hypotenuse.
4. We know that the opposite side is the vertical distance we want to find (the height), and the hypotenuse is the diagonal distance, which is the length of the hypotenuse of the triangle.
5. To find the length of the hypotenuse, we can calculate the horizontal distance AJ punted the ball. Since AJ was at the 10-yard line, and the TV screen starts at the 40-yard line, the horizontal distance is 40 - 10 = 30 yards.
6. Now we have all the information we need to calculate the height:
sin(70 degrees) = height / hypotenuse.
sin(70) = height / 30.
7. Rearrange the equation to solve for the height:
height = sin(70) * 30.
8. Calculate the height using a scientific calculator or trigonometric table.
height ≈ 27.83 yards.
Therefore, the height of the video screen suspended above the field is approximately 27.83 yards.