pythagorean theorem
The Pythagorean Theorem states that:
This equation is used to find an unknown value of a side of any right triangle. In a right triangle, there are two legs, which are the sides that form the right angle, and the hypotenuse, the remaining side, which is in a diagonal position. The formula shown above is designed to find the hypotenuse.
|
SIDES OF A RIGHT TRIANGLE
a = leg
b = leg c = hypotenuse |
formula for an unknown value of a leg
Although the original formula in the pythagorean theorem is designed to find the unknown value of a hypotenuse, it can be modified to find an unknown value of a leg. The formula would be the following: The same values are used, but the squared value of the hypotenuse is subtracted from the one from a leg, to find the value of the missing leg.
|
problem solving (word problems)
There are many ways in which Pythagoras can be applied to word problems. They mostly involve objects that form a right triangle in any way, and there is an unknown value. To solve these, first recognise which is the unknown value (hypotenuse of leg), to then substitute the values that are given to you in the problem, and use the formula to find the missing value.
*Always remember to write the correct measurement in your answer (inches, centimetres, etc) EXAMPLE: An 8 m long ladder has its feet placed 3 m out from a vertical wall. How far up the wall will the ladder reach? |
Haese and Harris (Page 206)
|
Unit reflection
I consider this short unit one of the easiest, compared to the other ones. Although Pythagoras or the pythagorean theorem are some things that I haven't studied before, there were a few steps to follow in every problem. Using the formula, substituting the values, to then find the measurement of the unknown side, were simple steps that I followed carefully, although at first I would make small mistakes and ended up with a wrong answer. As I practiced more of these, they were simple to understand. The only problem I had in this unit were simplifying radicals, when the answer was not a perfect square. I had some trouble with these in the last unit, but in this unit I was able to get better at it and understood completely the concepts it included.
***REAL LIFE APPLICATION: I used the pythagorean theorem in Un Techo Para Mi País, in April. Before building the house, we had to make sure that the borders and perimeter made a rectangle with right angles. So we had to measure the two "legs" of the triangle, and use the formula to determine if the hypothalamus was the correct one, which would made a right triangle.
***REAL LIFE APPLICATION: I used the pythagorean theorem in Un Techo Para Mi País, in April. Before building the house, we had to make sure that the borders and perimeter made a rectangle with right angles. So we had to measure the two "legs" of the triangle, and use the formula to determine if the hypothalamus was the correct one, which would made a right triangle.