Final answer:
To determine the bird's approximate height above the ground, we can use trigonometry. The tangent of the angle 40° is equal to the opposite side (height of the bird) divided by the adjacent side (distance from the child's eyes to the bird). Solving for the height, we find that the bird's approximate height above the ground is approximately 9.8 feet.
Step-by-step explanation:
To determine the bird's approximate height above the ground, we can use trigonometry. Since the child's eyes are 4 feet above the ground and 12 feet from the bird, we can form a right triangle with the child's eyes as one vertex, the bird as another vertex, and a point directly below the bird as the third vertex. The angle between the child's line of sight and the ground is 40°.
We can use the tangent function to find the height of the bird above the ground. The tangent of the angle 40° is equal to the opposite side (height of the bird) divided by the adjacent side (distance from the child's eyes to the bird). We can set up the equation as:
tan(40°) = height / 12
Solving for the height, we get:
height = 12 * tan(40°) ≈ 9.8 feet
Therefore, the bird's approximate height above the ground is approximately 9.8 feet.