A kite flier wondered how high her kite was flying. She used a protractor to measure an angle of 36 degrees from level ground to the kite string. If she used a full 140-yard spool of string, how high, in feet, was the kite? (Disregard the string sag and the height of the string reel above the ground.)

Round your answer to three decimal places.

Height = ___feet

h/140 = sin 36°

gives the height in yards

To find the height of the kite, we can use the trigonometric function tangent (tan). The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the opposite side is the height of the kite and the adjacent side is the length of the string. We can set up the equation as follows:

tan(36 degrees) = height of the kite / 140 yards

To solve for the height of the kite, we need to convert the yards to feet, as follows:

1 yard = 3 feet

Therefore, 140 yards = 420 feet.

Now we can substitute the values into the equation:

tan(36 degrees) = height of the kite / 420 feet

To find the height, we can isolate the variable by multiplying both sides of the equation by 420 feet:

height of the kite = tan(36 degrees) * 420 feet

Using a scientific calculator, we can find the value of tan(36 degrees) to be approximately 0.7265.

Now we can substitute this value into the equation:

height of the kite = 0.7265 * 420 feet

Calculating this, we find that the height of the kite is approximately 305.61 feet.

Round this to three decimal places:

Height = 305.610 feet.

Therefore, the height of the kite is approximately 305.610 feet.

To find the height of the kite, we can use trigonometry and set up a right triangle. Let's assume that the height of the kite is represented by the vertical leg of the triangle, and the length of the string is represented by the hypotenuse. The angle measured from the ground to the kite string gives us the angle between the vertical leg and the hypotenuse.

From the given information, we have:
Angle (θ) = 36 degrees
Length of string (hypotenuse) = 140 yards

Since the length of the string is given in yards, let's first convert it to feet. There are 3 feet in 1 yard, so the length of the string in feet is:
140 yards x 3 feet/yard = 420 feet

Next, we can use the trigonometric function tangent (tan) to find the height of the kite. The tangent of an angle in a right triangle is the ratio of the opposite side (height) to the adjacent side (length of string).

tan(θ) = height / length of string

Plugging in the values:
tan(36 degrees) = height / 420 feet

To solve for the height, we rearrange the equation:
height = tan(36 degrees) x 420 feet

Now, let's calculate the height using a scientific calculator or a calculator app:

height ≈ tan(36 degrees) x 420 feet
height ≈ 0.726542528 x 420 feet
height ≈ 304.108 feet

Rounding to three decimal places, the height of the kite is approximately 304.108 feet.

Therefore, the answer is:
Height = 304.108 feet