10th GRADE
Measuring Your World
The Pythagorean theorem applies to all right triangles when you apply a squared plus b squared equals c squared, adjacent and opposite squared always equals the hypotenuse. To use this to find distance you make a right triangle out of the line and then use the theorem. to find the equation of a circle you must use the distance formula so you make a right triangle and then plug the things in to the formula witch is x squared plus y squared equals r squared. x and y are the coordinates of the point and r is the radius. A unit circle is a circle centered at the origin of the coordinate plane with a radius of one. to find points on a 45 degree unit circle you have to make a right triangle and then lable everything you know about it and use the equation x sq plus y sq equals r sq and since r is 1 it is now x sq + y sq = 1 also since both the angles are 45 x and y are equal so you can do this.
Then we have to put the radical sign in the numerator and this is how you do that.
So then you label that on the point on the unit circle. The way you find points on the unit circle at 30 degrees is to start the same way as the other on but we cant use the equation yet because we have no clue what the side lengths are so you have to reflect it across the x axis to make an equilateral triangle since this is an equilateral triangle all the sides are the same so now you cut that length in half and get y2 so the triangle looks like this.
Then you can use the equation to find the point.
In this project I decided to measure a water tank because it seemed interesting to find its volume.
I was going to go to a water tank and then use a protractor and a weight tied to it and then point the protractor towards the tank afound the measurements of the tank online