a girl lets out 50 yards of kite string while flying a kite. The distance from a point on the ground directly under the kite to where she is standing is 30 yards. if the girl holds the string 3 feet from the ground how high is the kite? assume the string is tight.
The first thing you want to do is draw a picture of this. It will help you learn why you are doing these equations.
In the picture, you will have a kite in the air. It will be attached, by a string, to a girl. The girl is not below the kite, but off to the side.
The string is 50 yards. So write 50 next to that string.
You are looking for the height of the kite. So draw a line from the kite to the ground. Put a question mark there, since that is what we are looking for.
Now, draw a line from the string (not the girl's feet) to that line with the question mark. We know this distance is 30 meters.
Draw a line from where the girl is holding the string to the ground. This is 1 meter (3 feet). So write that in.
Do you see what we have now? We have a right angle triangle sitting on top of a rectangle that is a meter tall.
Now, let's figure out what that question mark is. This will tell us the height from the kite to where the string is.
Do you remember a^2 + b^2 = c^2?
We know what a and c are. Let's put those in.
30^2 + b^2 = 50^2.
900 + b^2 = 2500
b^2 = 1600
b = 40
So the distance between the kite and the height of the string (not the ground) is 40 meters.
The only catch here is that extra meter off the ground. Add that in.
Total height = 41 meters.
Keep doing drawings until you can visualize these in your head. After that, things become easier and you'll begin to just know the process.
If you do it without the drawings, it is usually harder to learn.
40.7
To find the height of the kite, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the kite will be one of the sides of the right triangle, the distance from the girl's hand to the ground will be the other side, and the length of the string will be the hypotenuse.
Let's solve the problem step by step:
1. Convert the length of the string from yards to feet:
50 yards = 150 feet
2. Set up the equation using the Pythagorean theorem:
(Height)^2 + (Distance from hand to ground)^2 = (Length of string)^2
Let "h" represent the height of the kite, and "d" represent the distance from the girl's hand to the ground. We have the following equation:
h^2 + d^2 = 150^2
3. Substitute the given values into the equation:
h^2 + 30^2 = 150^2
Simplify:
h^2 + 900 = 22500
4. Rearrange the equation to solve for height:
h^2 = 22500 - 900
h^2 = 21600
5. Take the square root of both sides to find the height:
h = √21600
6. Use a calculator to find the square root of 21600:
h ≈ 146.97
Therefore, the height of the kite is approximately 146.97 feet.
To determine the height of the kite, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance from the girl's position to the point directly under the kite on the ground is 30 yards (base of the triangle), and the length of the kite string is 50 yards (hypotenuse). We need to find the height of the kite (opposite side of the triangle).
Using the Pythagorean theorem, we have:
Base^2 + Height^2 = Hypotenuse^2
30^2 + Height^2 = 50^2
900 + Height^2 = 2500
Height^2 = 1600
Height = √1600
Height = 40 yards
Therefore, the kite is approximately 40 yards high.