Pythagorean Quadratic Essay
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The Pythagorean Theorem was termed after Pythagoras, who was a well-known Greek philosopher and mathematician, and the Pythagorean Theorem is one of the first theorems identified in ancient civilizations. “The Pythagorean theorem says that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse” (Dugopolski, 2012, p. 366 para. 8). For this reason, many builders from various times throughout history have used this theorem to assure that their foundations were laid out with right angles.
In this assignment, we will use the example of locating a treasure using two different treasure maps as the two points needed to determine how many paces it will take to find the exact location to start digging for treasure. For this assignment, we are given instructions to solve problem number 98 from page 371 in Elementary and Intermediate Algebra, which states that Ahmed’s treasure map specifies that the treasure can be found 2x +6 steps from Castle Rock and Vanessa’s half indicates to walk x steps heading north, then 2x + 4 steps toward the east (Dugopolski, 2012).
We need use the Pythagorean Theorem to figure out what variable x would be if they were to work together and combine their information. The Pythagorean Theorem indicates that a right triangle has legs with the length of a and b and the longest side of the triangle, the hypotenuse, as the length of c. Thus, the relationship with these lengths is the short equation of a2 + b2 = c2 (Dugopolski, 2012). Let a = x (x-10)(x+2)=0 Now, we solve each binomial using the zero factor x – 10 = 0 or x + 2 = 0 property in order to create a compound equation.
x = 10 or x = -2Answer to the equation. The issue now is that one of the answers is extraneous, because it does not satisfy this specific scenario. The reason for this is that logically we would not take negative steps to reach a certain point or in a geometric situation, we cannot move a negative distance (Dugopolski, 2012). This means that -2 will not work for this equation, so the only answer we are left with is x = 10 paces. In summary, Vanessa’s portion of the map tells us that the treasure is located 10 paces north and 2x + 4 = 2(10) + 4= 24 paces east of Castle Rock.
While Ahmed’s map tells us to take 2x + 6 = 2(10) + 6= 26 paces heading directly towards the rock. The Pythagorean Theorem is a very useful tool when we have a right-angled triangle and know the lengths of at least two sides, because it enables us to determine the length of the third side. On television, many of us have seen how important determining the trajectory of a bullet is to a crime scene, so it would be extremely critical to understand this theorem if your career was as a crime scene investigators.
Another career that uses this theorem is an architect who would use this for a home’s triangular rooftop. One of the more commonly every day uses is with navigation, although many of us simply rely on our navigational systems, we could still pinpoint our location if we have two points to start with. ? Reference Dugopolski, M. (2012). Elementary and Intermediate Algebra (4th ed. ). New York, NY: McGraw-Hill Publishing.