Practice Using the Pythagorean Theorem to Find Missing Sides of Right Triangles: Grade 8 Lesson Plan

Use the Pythagorean Theorem to solve each of the problems.

Learning Objective: The lesson is aligned to the Common Core State Standards for Mathematics – 8.G.7 Geometry – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Materials Required: graph paper, calculator

Lesson Procedure

LegsRightTriangle

Two-Dimensional Figures

  1. The triangle shown here is a right triangle.
  2. Side a equals 10 meters.
  3. Side b equals 6 meters.
  4. Use the Pythagorean Theorem a2 + b2 = c2, to find the length of side c of the right triangle. Calculate the length to the nearest tenth.

Answer: 11.7 meters

Three Dimensional Figures

  1. RectangularBox 1.jpg

    The dimensions of a rectangular box are 4 cm x 5 cm x 3 cm. What is the length of the longest pole you could fit in the rectangular storage unit?

  2. Let a = 4 cm, b = 5 cm, and c = 3 cm.
  3. Use the formula = + + , to find the length of the longest pole (x). Calculate the length to the nearest tenth.

Answer: 7.1 centimeters

Individual or Group Work:

Questions 1 – 4. Triangles drawn below are right triangles. Find the missing length for each right triangle. Calculate the length to the nearest tenth.

Right Triangles

5. The dimensions of a rectangular storage unit are 4ft x 8ft x 2ft. What is the length of the longest pole you could fit in the rectangular storage unit? Calculate the length to the nearest tenth.

Rectangular Box with Feet Measurement

6. The dimensions of a rectangular juice box are 12 cm x 5 cm x 3 cm. What is the maximum length of a straw from the flex part of the straw to the end of the straw that can be used in the juice box? Calculate the length to the nearest tenth.

Rectangular Box with CM Measurement

Students should be able to apply the Pythagorean Theorem, a2 + b2 = c2 to determine unknown side lengths in right triangles in real-world problems with two-dimensional and three-dimensional figures.

Answers

  1. Rectangle 1: 8.6 feet
  2. Rectangle 2: 8.2 feet
  3. Rectangle 3: 9 meters
  4. Rectangle 4: 16 meters
  5. Rectangular Storage Unit: 9.2 feet
  6. Rectangular Juice Box: 13.3 centimeters

This post is part of the series: Teaching the Pythagorean Theorem.

This series of lesson plans is intended for an eighth grade math class. Find a series of lessons that will teach your students about the Pythagorean theorem.
  1. Lesson 1: Explaining the Proof of the Pythagorean Theorem
  2. Lesson 2: Finding the Missing Lengths using the Pythagorean Theorem
  3. Lesson 3: Protecting the Castle using the Pythagorean Theorem
  4. Lesson 4: Hunting for Treasure using the Pythagorean Theorem
  5. Lesson 5: Playing a Video Game using the Pythagorean Theorem