# Pythagorean Theorem Foundations of Technology Pythagorean Theorem © 2013 International Technology and Engineering Educators Association, STEM  Center.

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• Foundations of Technology

Pythagorean Theorem 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology Teacher Resource Unit 2 Lesson 1

STEMCenter for Teaching and Learning

• The BIG IdeaBig Idea:

The Engineering Design Process is a systematic, iterative problem-solving methodthat produces solutions to meet human needs and wants.

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• RationaleEngineers 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.

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Pythagorean TheoremThe 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: a + b = c Where c is the hypotenuse and a and b are the adjacent sides

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

Hypotenuse (c)Right (90) AngleAdjacent Sides (a + b)

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Practice ProblemsSolve for the unknown variable:

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

c = ____a = 4inb = 3in

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Practice ProblemsSolve for the unknown variable:

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

c = 5ina = 4inb = 3inc = a + b

c = (4in) + (3in) c = 16in + 9in

c = 25in

c = 25in

c = 5in

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Practice ProblemsSolve for the unknown variable:

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

c = 15ina = ____b = 9in

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Practice ProblemsSolve for the unknown variable:

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

c = a + b

c - b = a

a = (15in) - (9in) a = 225in - 81in

a = 144in

a = 144in

a = 12in

c = 15ina = 12inb = 9in

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Practice ProblemsSolve for the unknown variables:

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

a = 12inb = 10inc = ______

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Practice ProblemsSolve for the unknown variables:

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

c = a + b

c = a + (b)

c = (12in) + (5in) c = 144in + 25in

c = 169in

c = 169in

c = 13in

c = 13ina = 12inb = 10in

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Calculate the total amount of material required to construct the crane boom:

Practice Problems 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• b1 = 15 cm Calculate the total amount of material required to construct the crane boom:

Practice Problems 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

a = 10 cm b2 = 30 cm b3 = 40 cm c1 = _____c2 = _____

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Calculate the total amount of material required to construct the crane boom:

Practice Problems 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

c = a + b

c1 = (10cm) + (15cm)c1 = 100cm + 225cmc1 = 325cmc1 = 325cmc1 = 18.0cm

c2 = (10cm) + (10cm)c2 = 100cm + 100cmc2 = 200cmc2 = 200cmc2 = 14.1cm

b1 = 15 cm b2 = 30 cm b3 = 40 cm c1 = 18.0cma = 10 cm c2 = 14.1cm

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

• Calculate the total amount of material required to construct the crane boom:

Practice Problems 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology

SegmentsQuantityLength (total)a330cmb2130cmb3140cmc1236cmc2114.1cmTotal:150.1cm

2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning Foundations of Technology