## Pythagorean Theorem Word Problems

#### Aligned To Common Core Standard:

**Grade 8 Geometry** - 8.G.B.8

Tips for Solving Pythagorean Theorem Word Problems -
When it comes to solving a triangle, there are a number of formulae and theorems that we bring into use. A theorem that helps us find a missing side of a triangle; Pythagorean theorem, also known as Pythagoras' theorem. The theorem provides a fundamental relationship between the base, height, and hypotenuse of a triangle. It is given by the equation;
(Hypotenuse)^{2} = (Base)^{2} + (Height)^{2}
The hypotenuse is always the longest side of the triangle.
After reading the problem, always start by creating a diagram.
Always try to identify the sides of a triangle before applying the theorem.
The theorem only applies to right-angled triangles.
You can make the missing side the subject of the equation to make the solution simple.
Memorizing the squares of numbers can help in reducing the overall time one takes to solve the problem. To check if you are going in the right direction, compare the calculated value of hypotenuse, it should always be greater than base and height.
These worksheets will help students learn how to solve word problems where they can utilize the use of the pythagorean theorem.

### Printable Worksheets And Lessons

- How Far Is John? Step-by-Step Lesson- John rides away in two directions. How far is he from his starting point?
- Guided Lesson - This one starts out really bland and then picks it up as we get further with it.
- Guided Lesson Explanation - It gets somewhat repetitive and even easier after number two.
- Practice Worksheet - I love the Tommy Turtle problem. My grandkids came up with all the names.
- Matching Worksheet - You can use the units to steer you in the right direction.

#### Homework Sheets

You will find many map skills based questions. Coordinate mapping goes right in stream here.

- Homework 1 - Alexander has a city map. He moves 18 meters north, then he moves 12 meters east. This is where he finds the shop he was looking for. Find the distance between Alexanderâ€™s initial location and the shop.
- Homework 2 - City A is 10 miles from city B, and 5 miles from city C. City A, B and C form a right triangle at A. A road connects cities B and C directly. Find the length of this road.
- Homework 3 - James saw a tree from a 6 meter distance. The tree is 7 meters long. Find the slope distance between the tree and James.

#### Practice Worksheets

Find the hypotenuse, traveling word problems, and find the triangle leg problems.

- Practice 1 - Find the hypotenuse of an isosceles triangle with a base of 10 cm and height of 10 cm.
- Practice 2 - Nathan leaves the house to go to the office. He walks 50 m west and 30 m north. Calculate how far he is from his starting point.
- Practice 3 - Find the height of a triangle that has a 5 cm width and has a hypotenuse of 20 cm.

#### Math Skill Quizzes

All the skills that we covered are scattered throughout the quizzes.

- Quiz 1 - Find the width of a triangle that has a 3 cm height and a hypotenuse of 4 cm.
- Quiz 2 - Find a, when b=10, c=11
- Quiz 3 - We can use the Pythagorean Theorem to find the missing side. The missing side is the hypotenuse (C when using the Pythagorean Theorem).

### Where Will You Come Across Pythagorean Theorem Word Problems Like This in Real Life?

Understanding right triangle geometry is much more impacting than you could ever imagine. This theorem has some many different applications that it is not even funny. As long as you can establish a single right angle, you can model a diagram that you can better understand with this in mind. When you are given two straight lines that meet at a right angle, you have a great deal of power. Almost all building and home construction is built off of this theorem. This ensures that structures are level and square. This starts when they begin to pour the foundation all the way until they are putting the last piece of sheetrock up. I have taken part in building three decks in my life. If I only had a nickel for each of the times, I referred back to using the Pythagorean theorem to determine if something was level of connecting! I would have a lot of nickels. This concept also extents itself to navigation of all types when we are dealing with vehicles travelling in fixed directions, we can determine how long it will take them to travel. This bring us to the old problem of two trains that start at the same point and go in different directions we then need to calculate how far apart those trains are.