Skill14 pythagorean
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The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. The document provides examples of using the Pythagorean theorem to find the missing side of a right triangle when given the other two sides. It also notes that word problems may present the theorem in applied contexts.
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Skill14 pythagorean
- 1. Skill14 Pythagorean Equation for Right Triangles Look at page 96 in your book.
- 2. The Pythagorean principle helps us find missing sides of a right triangle. Look at the triangle on the left. Notice the brace showing the right angle. The two sides that meet to form the right angle, a and b, are called the legs. The side opposite the right angle, c, is the longest side in the triangle and is called the hypotenuse. We can say then that the lengths of the sides are related in this way: Square the leg lengths and add them together. Their sum equals the square of the longest side, the hypotenuse. Look at the triangle on the right. The legs are 5 and 12. See the equation at the right. Square 5 and add it to the square of 12. That equals the square of 13. In a problem, one of these three numbers will be missing. The problem is to find it.
- 3. Finding the hypotenuse. Note that the letters do not have to be a, b, and c. Just look for the legs and the Hypotenuse . Here the hypotenuse is x.
- 4. Finding a leg. Here the missing leg is called y. See the formula in terms of the legs and hypotenuse. This is a little harder to do than finding the hypotenuse.
- 5. Be ready for this to be put in the form of a word problem. See below.
- 6. Another word problem. Study pages 96, 97, and 98.