PT4
- 1. The Pythagorean Theorem What it is and how it can be used
- 2. What it is: In about 580BC a Greek mathematician named Pythagoras discovered a method that can be used to determine whether triangles are right angle triangles. Today his method is known as: The Pythagorean Theorem
- 3. How it is used Pythagorean theorem states that a(altitude of triangle)squared + b(base of triangle)squared = c(hypotenuse of triangle)squared (a ² + b² = c²) The hypotenuse is the ‘shortcut’ angle on the triangle:
- 4. Using the Pythagorean Theorem Here is an example of how to use the Pythagorean theorem: Lets say a triangle has an altitude of 35m, a base of 12m, and a hypotenuse of 37m To determine whether the triangle is a right angle, square each measurement and use Pythagoras's formula: 35m²+12m²=37m²(1225m+144m=1369m) Find the square route of 1369m= 37m Because the measurements add up exact this triangle is a right angle
- 5. Solving Problems Using the Pythagorean Theorem You can also use the Pythagorean Theorem to solve problems as well. In this problem the hypotenuse is missing: If a triangle has an altitude of 45m and a base of 36m, what is the hypotenuse? 45m ²+36m²=c² (2025m+1296m=3321m) Now just find the square route of 3321m and you have figured out the hypotenuse of that triangle= 57.63m
- 6. Another Problem Sometimes, instead of finding the hypotenuse of the triangle you have to find the altitude or the base. If a triangle has a base of 25m and a hypotenuse of 40m, what is the altitude? a ²+25m²=40m² (a²+625m=1600m) Now you can solve the problem just like a type one algebra equation a²=1600m-625m(975m) If a² is 975m then just square route 975m to get about 31.22m (the triangle’s altitude)
- 7. The Pythagorean Theorem By Ryan Best I hope you can now understand not only what the Pythagorean Theorem is but also how to use as well. Thank you for watching.