Overview |
This semester's unit covered multiple things that connect with measurement. As a class, we started with the Pythagorean Theorem. Learning how to measure simple distances using triangles that lead to distance formula. Using the distance formula we began to explore what shapes would look like if they all had the same distance to a center point. Which then lead to creating a circle. One important piece of information we learn was, a circle will always have the same radial distance to each of its points. Then we transitioned to points on the x and y axis and how they' relate. Intersections with radial lines, and how or what angles are formed.
Which taught us about the Sine and Cosine of triangles. The Sine is the ratio between the hypotenuse and opposite sides of triangles. The Cosine is the ratio between the adjacent and hypotenuse sides of triangles. We learned how to apply these terms to the Pythagorean Theorem and the distance formula. By learning all this, we were able to start proving that a tangent of an angle is equivalent to sin/cos. Starting with 30, 45, 60 degree angles. In the final trigonometry portion, we were given a problem about how the British calculated the height and position of Mount Everest using a theodolite. After exploring trigonometry, we looked closer at polygonal equations. Using the Habits of a Mathematician "starting small" we were able to learn and understand how trigonometry played into this. Learning how a square can be split into right triangles. Leading into further exploration of using trigonometry to find areas of equilateral and isosceles triangles. Which helped us create formulas for pentagons, hexagons, septagons, octagons, and so onto x-gons where x is any value. To finish up the content part of this project, we learned about volume in 3d shapes and learning how to calculate the area and volume within shapes like rectangular prisms and cylinders. |
Math ConceptsContinue throughout the slideshow to find the process of solution
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