Final answer:
To calculate the height of the kite from the ground, we use the sine of the angle of elevation (53 degrees) with the length of the string (32 ft) to find the vertical distance from Sara's eyes to the kite, and add Sara's eye-level height to this distance.
Step-by-step explanation:
To determine how far off the ground Sara's kite is, we should consider the angle of elevation and the length of the kite string. The situation described forms a right triangle with the string of the kite as the hypotenuse, Sara's height as one part of the triangle, and the vertical distance from the top of Sara's head to the kite as the other part.
Since the string is 32 ft long and the angle of elevation is 53 degrees, we can use trigonometric functions. Specifically, the sine of the angle of elevation will be equal to the opposite side (the vertical distance from Sara's eyes to the kite) divided by the hypotenuse (the length of the string)
sin(53°) = opposite/hypotenuse
sin(53°) = vertical distance/32 ft
We can solve for the vertical distance by multiplying both sides of the equation by the length of the string:
vertical distance = sin(53°) × 32 ft
Now, to find the overall height of the kite above the ground, we must add Sara's height to the vertical distance calculated. Sara is 5 ft tall, and since her eyes are not at the very top of her head, let's estimate the height from her eyes to be approximately 4.5 ft.
Total height of kite from ground = 4.5 ft + (sin(53°) × 32 ft).