When I went kite flying the other day, I let out an entire roll of string (400 feet). If when the string pulled tight formed a 40 degree angle with the ground, about how high was the kite?
Draw a diagram and hence deduce that
Height=400 sin(40°)
40% of an obtuse decathlon
To determine the height of the kite, we can use trigonometry and the given information about the length of the string and the angle it forms with the ground.
We can start by visualizing the situation. Imagine a right-angled triangle where the string acts as the hypotenuse, the height of the kite is the opposite side, and the distance between you and the kite is the adjacent side. The angle between the ground and the string is 40 degrees.
Now, we can use the trigonometric function "sine" to find the height of the kite. The sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side represents the height of the kite, and the hypotenuse is the length of the string.
The formula to find the height is:
height = string length * sine(angle)
Plugging in the values we have:
height = 400 feet * sine(40 degrees)
To calculate this, you can use a scientific calculator capable of evaluating trigonometric functions. Here's how you can do it step by step:
1. Set your calculator to degree mode.
2. Enter the value of 40 degrees.
3. Press the "sine" function button. This will give you the value of sine(40).
4. Multiply the result by 400 feet.
5. The final result will give you the approximate height of the kite.
So, using this method, you can find out the height of the kite by multiplying the length of the string by the sine of the angle formed with the ground.