. Exercise: Week Six Concept Check
The theorem works In any right triangle. A key observation is that a and b are at right angles. Movement in one direction has no impact on the other. The Pythagorean Theorem can be used with any shape and for any formula that squares a number. The Pythagorean Theorem lets you use find the shortest path distance between orthogonal directions. So it’s not really about right triangles — it’s about comparing “things” moving at right angles. The area of any shape can be computed from any line segment squared. In a square, our "line segment" is usually a side, and the area is that side squared (side 5, area 25). In a circle, the line segment is often the radius, and the area is pi * r^2 (radius 5, area 25 pi).
The Pythagorean Theorem is used in real life in many different ways. Nova Online demonstrates two real world applications in particular. One involves throwing a runner out from home plate and the other involves climbing a ladder up the side of a house.
There are many applications for the Pythagorean Theorem. For example, it can be used to find the distance between two cities given a reference city, the length of an edge in a right triangle if you are building a house, the magnitude of the velocity of a projectile given its horizontal and vertical speeds, and to find real power versus complex power for electronic utility companies. You are at your grandma's house for the weekend but you've decided you're ready to go home. Your mom says the only way you can come home is if you tell her exactly how many miles is the shortest distance from Grandma's before you can leave. She tells you that your street and Grandma's street meet to form an L at your school. Grandma's house is two miles east of the your school and your house is one mile north of your school. She also tells you the shortest distance home does not involve passing your school again....
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