Posted by ryhane on .
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.
pre algebra -
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.
pre algebra -