kelly is flying a kite using 223 ft. of string. the angle of elevation of the kite is 42 degrees. Find the horizontal distance from kelly to the point directly below the kite. The find the height of the kite.
To find the horizontal distance from Kelly to the point directly below the kite, we need to use trigonometry.
Let's call the horizontal distance x. We know that the angle of elevation of the kite is 42 degrees, so the angle between the string and the ground is also 42 degrees.
Using the definition of tangent, we can set up the following equation:
tan(42°) = height of the kite (in this case, x) / length of the string
tan(42°) = x / 223ft
To solve for x, we can rearrange the equation:
x = 223ft * tan(42°)
x ≈ 223ft * 0.9004
x ≈ 200.5ft
The horizontal distance from Kelly to the point directly below the kite is approximately 200.5ft.
To find the height of the kite, we can use the definition of sine.
sin(42°) = height of the kite / length of the string
sin(42°) = height of the kite / 223ft
To solve for the height of the kite, we can rearrange the equation:
height of the kite = 223ft * sin(42°)
height of the kite ≈ 223ft * 0.6691
height of the kite ≈ 149.1ft
The height of the kite is approximately 149.1ft.