Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems.

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Presentation transcript:

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems using the Pythagorean Theorem Right Angle: angle that forms 90° Hypotenuse: in a right triangle, it is the side opposite the 90° angle Leg: each of the sides forming the right triangle Pythagorean Theorem: describes the relationship of the lengths of sides of a right triangle.

The Pythagorean Theorem 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. . . a2 + b2 = c2 c (hypotenuse) This is a right triangle a (leg) 90° b (leg) a and b are the legs of the right triangle This is NOT a right triangle c is the hypotenuse and is ALWAYS the longest segment

The Pythagorean Theorem What is the length of the hypotenuse of this triangle? Step 1. Write the formula for the Pythagorean Theorem. Step 2. Substitute in known values. Step 3. Solve for the unknown variable.

Real-world Pythagorean Theorem A television screen measures approximately 15.5 in. high and 19.5 in. wide. A television is advertised by giving the approximate length of the diagonal of its screen. How should this television be advertised? Draw and label a diagram to model the problem. c 15.5 19.5 Solve for c, using the Pythagorean Theorem. The television should be advertised as a 25”.

Real-world Pythagorean Theorem A toy fire truck is near a toy building on a table such that the Base of the ladder is 13 cm from the building. The ladder is extended 28 cm to the building. How high above the table is the top of the ladder? Draw a diagram to model the problem. Solve using the Pythagorean Theorem The truck is approximately (24.8 + 9) 33.8 cm above the table.

Converse of the Pythagorean Theorem If a triangle has sides of length a and b, and a2 + b2 = c2, then the triangle is a right triangle with hypotenuse of length c. Remember, c is the longest side in a right triangle. Determine whether the given lengths are sides of a right triangle. a. 5 in., 5 in., and 7 in. Not a right triangle b. 10 cm, 24 cm, and 26 cm This is a right triangle

Physics and the Pythagorean Theorem If two forces pull at right angles to each other, the resultant force is represented as the diagonal of a rectangle, as shown in the diagram. The diagonal forms a right triangle with two of the perpendicular sides of the rectangle. For a 50–lb force and a 120–lb force, the resultant force is 130 lb. Are the forces pulling at right angles to each other? Yes, the forces are pulling at right angles to each other.