A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60 degrees with the horizontal. Approximate the height of the kite above level ground if 500 feet of string is payed out.
Height= 4ft + 500cos60
Does that make sense?
Yes it does. I will multiply cos60 which is 1/2 by 500 and add 4 feet. And I would use cos because it is adj/hyp. Is that a fairly good explanation?
Since the angle is 60° with the horizontal, shouldn't that be 4'+500sin(θ) for the height?
yes its 4'+500sin(60)
To approximate the height of the kite above level ground, we can use trigonometry and the given information about the angle and length of the string.
First, let's draw a diagram to visualize the situation:
```
KITE
/|
/ |
/ | h (height of the kite above ground)
/ |
/ | 60°
/_____|
GROUND
```
We know that the person holding the string is standing 4 feet above the ground, so we can think of the length of the string as the hypotenuse of a right triangle. The height of the kite (h) will be the opposite side, and the horizontal distance from the person to the kite will be the adjacent side.
Next, we can use the trigonometric ratio for sine to find the height of the kite:
sin(60°) = opposite/hypotenuse
sin(60°) = h/500ft [Since the hypotenuse is given as 500ft]
Now, we can solve for h by rearranging the equation:
h = 500ft * sin(60°)
h ≈ 500ft * 0.866 (using the approximate value of sin(60°) as 0.866)
h ≈ 433ft
Therefore, approximately, the height of the kite above level ground is 433 feet.