Final answer:
To determine the height of the kite above the ground, we use the sine function in trigonometry with the given angle of 42 degrees and the kite string length of 60 feet, resulting in an approximate height of 40.15 feet.
Step-by-step explanation:
To find how high above the ground the kite is, we need to use trigonometry. The kite string makes an angle of 42 degrees with the ground, and we can imagine a right triangle where the kite string is the hypotenuse, the height above the ground (h) is the opposite side, and the distance along the ground from the person holding the kite to a point directly below the kite is the adjacent side.
We use the sine function, which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. The formula is:
sin(angle) = opposite/hypotenuse
For our problem, we have:
sin(42 degrees) = height/60 feet
Once we calculate sin(42 degrees), we multiply that value by 60 feet to find the height (h).
sin(42 degrees) ≈ 0.6691
height = 0.6691 × 60 feet
≈ 40.15 feet
Therefore, the kite is approximately 40.15 feet above the ground.