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**Unit 2: Engineering Design Process**

Foundations of Technology Unit 2: Engineering Design Process Lesson 1: Engineering Design Process Pythagorean Theorem

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The Big Idea Big Idea: The Engineering Design Process is a systematic, iterative problem-solving method that produces solutions to meet human needs and wants.

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Rationale Engineers use mathematical equations as tools to help them create technical solutions, structures, and products to meet the needs and desires of society. Throughout the Foundations of Technology course, students will apply mathematics to solve practical problems and work through design challenges. The Pythagorean Theorem is an excellent place to start because it applies simple logic and basic algebra.

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Pythagorean Theorem The Pythagorean Theorem applies to right triangles and states that the square root of the hypotenuse is equal to the square root of the sum of the squares of the adjacent sides. Algebraically: a² + b² = c² Where “c” is the hypotenuse and “a” and “b” are the adjacent sides Hypotenuse (c) Adjacent Sides (a + b) Right (90º) Angle

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**Practice Problems Solve for the unknown variable: c = ____ a = 4in**

b = 3in

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**Practice Problems Solve for the unknown variable: c² = a² + b²**

c² = (4in)² + (3in)² c² = 16in² + 9in² c² = 25in² √c² = √25in² c = 5in c = 5in a = 4in b = 3in

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**Practice Problems Solve for the unknown variable: c = 15in a = ____**

b = 9in

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**Practice Problems Solve for the unknown variable: c² = a² + b²**

c² - b² = a² a² = (15in)² - (9in)² a² = 225in² - 81in² a² = 144in² √a² = √144in² a = 12in c = 15in a = 12in b = 9in

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**Practice Problems Solve for the unknown variables: c = ______ a = 12in**

b = 10in

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**Practice Problems Solve for the unknown variables: c² = a² + b²**

c² = (12in)² + (5in)² c² = 144in² + 25in² c² = 169in² √c² = √169in² c = 13in c = ______ a = 12in b = 10in

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Practice Problems Calculate the liner amount of material required to construct the crane boom:

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Practice Problems Calculate the liner amount of material required to construct the crane boom: c2 = _____ c1 = _____ a = 10 cm b1 = 15 cm b2 = 30 cm b3 = 40 cm

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Practice Problems Calculate the liner amount of material required to construct the crane boom: c2 = 14.1cm c² = a² + b² c1² = (10cm)² + (15cm)² c1² = 100cm² + 225cm² c1² = 325cm² √c1² = √325cm² c1 = 18.0cm c2² = (10cm)² + (10cm)² c2² = 100cm² + 100cm² c2² = 200cm² √c2² = √200cm² c2 = 14.1cm c1 = 18.0cm a = 10 cm b1 = 15 cm b2 = 30 cm b3 = 40 cm

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Practice Problems Calculate the liner amount of material required to construct the crane boom: b1 = 15 cm b2 = 30 cm b3 = 40 cm c1 = 18.0cm a = 10 cm c2 = 14.1cm Segments Quantity Length (total) a 3 30cm b2 1 b3 40cm c1 2 36cm c2 14.1cm Total: 150.1cm

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The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.

The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.

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