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° with the horizontal (see the figure). Approximate the height of the kite above level ground if 500 feet of string is payed out. (Round your answer to one decimal place.)

Height= 4ft + 500cos60, multiply cos60 which is 1/2 by 500 and add 4 feet. Use cos because it is adj/hyp. Which is 4'+500sin(60)

Almost. Use sin60°, since we want the height, not the distance along the ground.

The ground is the "adjacent" side here.

h-4/700 = sin60°

To approximate the height of the kite above level ground, we need to use trigonometry. Let's refer to the height of the kite as "h".

In the given figure, we have a right triangle formed by the height of the kite, the horizontal distance from the person to the kite, and the string of the kite.

Using trigonometry, we can determine that the sine of the angle of elevation (60°) is equal to the opposite side (height of the kite) divided by the hypotenuse (string length). So, we have:

sin(60°) = h / 500 feet

The sine of 60 degrees is √3/2, so we can rewrite the equation as:

√3/2 = h / 500 feet

To solve for h, we can multiply both sides of the equation by 500 feet:

h = (√3/2) * 500 feet

Now, we can plug this into a calculator to find the approximate value:

h ≈ 866.025 feet

Therefore, the height of the kite above the level ground is approximately 866.0 feet.