Final answer:
To find the height of the blimp, we can use trigonometry to set up and solve equations. By using the tangent function, we can determine the height based on the given angles of depression and the horizontal distance between the goal posts. The height of the blimp is approximately 488.7ft.
Step-by-step explanation:
To solve this problem, we can use trigonometry. Let's assume the height of the blimp is h. We can set up a right triangle with one leg being the horizontal distance between the goal posts (360ft) and another leg representing the height of the blimp. The angle of depression to the base of one goal post is 40°, so the angle between the ground and the hypotenuse (the line from the blimp to the base of the goal post) is also 40°. Similarly, the angle between the ground and the hypotenuse for the other goal post is 72°.
Using the trigonometric function tangent, we can set up the following equations:
tan(40°) = h/x
tan(72°) = h/(x + 360)
Simplifying these equations, we get:
x = h/tan(40°)
x + 360 = h/tan(72°)
Substituting the first equation into the second equation, we get:
h/tan(40°) + 360 = h/tan(72°)
Solving for h, we find:
h = 360 * (1/tan(72°) - 1/tan(40°))
Using a calculator, the value of h is approximately 488.7ft. Therefore, the blimp is flying at a height of approximately 488.7ft.