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

2. 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.

3. 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.

4. 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

5. Practice Problems Solve for the unknown variable: c = ____ a = 4in
b = 3in

6. 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

7. Practice Problems Solve for the unknown variable: c = 15in a = ____
b = 9in

8. 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

9. Practice Problems Solve for the unknown variables: c = ______ a = 12in
b = 10in

10. 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

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

12. 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

13. 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

14. 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