Final answer:
The length of string Katie has released is 18.28 m.
Step-by-step explanation:
To solve this problem, we can use trigonometry, specifically the sine function, which defines the ratio between the opposite side of a right triangle and the hypotenuse. In this scenario, the 'opposite' is the vertical distance from Katie's hand to the kite (15m - 1m = 14m) and the 'hypotenuse' is the length of the string. We will set up our equation based on the given angle of 50 degrees.
The sine of the angle is equal to the opposite side divided by the hypotenuse:
sin(50°) = opposite/hypotenuse
Plugging in the values we have:
sin(50°) = 14m / hypotenuse
To find the length of the hypotenuse (the string), we rearrange the formula and solve:
hypotenuse = 14m / sin(50°)
= 18.28 m
The length of string Katie has released is 18.28 m.