Respuesta :
Answer:
To find out how high the rocket flew, we can use trigonometry. We'll consider the observer, the rocket, and the angle formed when the observer looks up at the rocket at its highest point. Here's how we can calculate the height of the rocket:
1. First, we can create a right triangle with the observer, the rocket, and the point on the ground directly below the rocket's highest point.
2. The angle of elevation is 78°, which means the angle between the ground and the observer's line of sight to the rocket is 78°.
3. Since the observer is standing 25 feet back and their eyes are 6 feet above the ground, the height of the observer's eyes above the ground and the horizontal distance to the rocket form a right triangle.
4. Using trigonometry, we can use the tangent function to find the height of the rocket. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side.
5. In this case, tan(78°) = height of the rocket / 25 feet. We can solve for the height of the rocket by rearranging the equation to find: height of the rocket = 25 feet * tan(78°).
6. By calculating 25 feet * tan(78°), we find that the rocket flew approximately 98.4 feet high (rounded to the nearest tenth of a foot).
Therefore, the rocket flew approximately 98.4 feet high into the air.
