# 2.7 Utility workers: Working with the Pythagorean theorem

Essential question: How is the Pythagorean theorem useful to utility workers?

## Learning outcomes

- Students will use the Pythagorean theorem to solve problems.
- Students will use proportions to convert from metric measurements to customary units.

## Teacher planning

### Materials needed

- Hurricane Rich worksheet (Includes answer key)
- Calculator

### Time required for lesson

Approximately 30 minutes

## Activities

- Review the Pythagorean theorem and what each variable represents. (5 minutes)
- Put students in pairs and hand out the worksheet, which presents the following scenario:

Hurricane Rich recently swept through the Carolinas, ripping many utility poles from the ground. Duke Power sent crews out immediately to restore power to the thousands of residents without electricity. As the crew members were replacing the broken poles, the lead crew member, Mark German, was calculating the length of the guy wire (the strong cable that provides support to a utility pole) that would be needed to support the utility poles more efficiently. If the guy wire with a length of 23.8 meters is attached to a utility pole and the wire is anchored to the ground 9 meters from the base of the pole, how high above the ground is the guy wire attached to the utility pole? Round your answer to the nearest tenth of a meter.

- Have students work in pairs to complete the worksheet. (15 minutes)
- Review the answers to the worksheet. Answer any questions that the students may have. (5 minutes)
- Discuss with students the careers of utility workers. (See “Career Information” below.)
- Conclude the lesson by brainstorming other possible careers that may use the Pythagorean theorem. (5 minutes) Examples may include:
- Farmers may need to know how much fencing would be needed in a field shaped like a right triangle
- Parasailing industry workers need to know how long the tow line should be under certain weather conditions
- Construction workers / firefighters may need to know the length of a ladder against the building either to paint or fight fires
- Outdoor events workers putting up tents need to know the length of support cables.

## Career information

Some of the information below comes from the Bureau of Labor Statistics’ Occupational Outlook Handbook.

- Utility workers
- Utility workers are responsible for the cables that provide electricity, phone service, and cable service to businesses and homes. The repair and maintenance of these cables can be located at the top of poles and towers that must be climbed. Many outages occur during storms, so the utility worker is on call at these times and expected to work overtime until the outages are fixed. High-voltage power lines and the height at which they work can make this a dangerous profession. Safety procedures must always be followed.
**Education**: High-school diploma**Pay**: $29,000 to $70,000**Growth**: Slower than average; 6% decrease in the next 10 years

- Construction workers
- There are many types of construction workers. Construction workers may work in carpentry, painting, electrical, or plumbing. Most are paid by the number of hours they work each week. The more specialized construction workers are, the higher their salary. Many jobs require work outside which is dependent on the weather. Bad weather can stop construction for a period of time which can stop or decrease income. Construction workers that specialize in carpentry frame new buildings. When framing the buildings, they can use the Pythagorean Triples to be sure the studs are set at right angles.
**Education**: High-school diploma**Pay**: $30,000 to $41,000**Growth**: Average growth; 10% increase in the next 10 years

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 9–12 — Algebra 1

**Goal 1**: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.**Objective 1.02**: Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.

**Goal 2**: Geometry and Measurement - The learner will describe geometric figures in the coordinate plane algebraically.**Objective 2.01**: Find the lengths and midpoints of segments to solve problems

- Common Core State Standards
- Mathematics (2010)
#### Grade 8

- Geometry
- 8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

- Geometry
#### High School: Geometry

- Similarity, Right Triangles, & Trigonometry
- GEO.SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

- Similarity, Right Triangles, & Trigonometry