Final Answers:
a) The height of the kite above the ground is approximately 23 meters.
b) The length of the string is approximately 35 meters.
c) The other friend is approximately 20 meters away from Carol.
Step-by-step explanation:
The height of the kite above the ground can be determined using trigonometry. Given the angle of elevation from one friend at 66°, the tangent function relates the height to the distance between Carol and the friend. Using tan(66°) = height / 11m, we solve for the height and find it to be approximately 23 meters.
To find the length of the string, consider the right-angled triangle formed by the kite, the ground, and the string. The sine function is applicable here as sin(50°) = height / length of string. Solving for the length of the string gives approximately 35 meters.
For the distance between the other friend and Carol, we use the angle of elevation of 35°. Employing the tangent function again, tan(35°) = height / distance, where the height is the same as previously calculated (23 meters). Solving for the distance gives approximately 20 meters.
In summary, the height of the kite above the ground is 23 meters, the length of the string is 35 meters, and the distance of the other friend from Carol is approximately 20 meters. These calculations are derived from the principles of trigonometry, considering the angles of elevation and the distances involved in the scenario.