# Finding Missing Sides of Triangles Worksheets

We are all aware of the that we can use the Pythagorean theorem (a^{2} + b^{2} = c^{2}) to determine the length of a missing side. This is where c is the value of the longest side. This is definitely very helpful for many situations; we will even practice it on this topic many times. There are few different methods that we can use to determine these sides as well. All triangles have three sides and angles for a total of six data points. The cool thing is that if you know any three of these six data points, you can determine the value of the other three. This will always work as long as you know the measure of one side, but always need at least one side to gauge how big the geometric shape is. These worksheets and lessons will help you learn how to find these missing measures with ease.

### Aligned Standard: Grade 8 Geometry - 8.G.B.7

- Raider Ron's Treasure Step-by-Step Lesson- Calculate how far Pirate Raider Ron is from his boat after an afternoon of treasure hunting.
- Guided Lesson - We start working with distances on maps. Move from city to city and determine how far you have moved.
- Guided Lesson Explanation - Pythagorean theorem helps us solve just about everything in this series.
- Independent Practice - I dreamed up some really unique situations where we could use right triangle theory.
- Matching Worksheet - All units were removed from the choices to make it more challenging. You could give students extra credit for adding units.
- The Pythagorean Theorem Five Pack - Find the third side.
- Mean Proportional in a Right Triangle Worksheet Five Pack - Find the missing sides of these back to back triangles.
- Mid-Segment of a Triangle Worksheet Five Pack - See if you can sense those missing parts now.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

These are basically Pythagorean Theorem application questions.

- Homework 1 - Rhino has a map of a hidden treasure. He moves 13 meters 90° south, then he moves 20 meters west. He finds the treasure hidden in a chest. Find the distance between Rhino's initial location and the hidden treasure.
- Homework 2 - There are 3 companies J, K, L in a large city. The companies are connected by roads forming a right triangle. The distance from J to K is 5 km and K to L is 6 km. Find the distance between J and L.
- Homework 3 - Janis makes a birthday card with paper for her friend's birthday. The height of the card is 20 centimeters and it is 8 centimeters long across the diagonal. Find the length of the base of the birthday card.

### Practice Worksheets

I tried my best to think up real life problems that use these skills.

- Practice 1 - We have a right triangle that has a 16 meter perpendicular side and a 19 meter leg. Find the hypotenuse.
- Practice 2 - Ryan is making a ramp. Find the length of the ramp if the height is 9 meters and the base is 27 meters.
- Practice 3 - Every Sunday Jonny goes to the florist from his home. He drives 10 miles north and then he turns east for another 5 miles. How much distance is between his home and the florist?

### Math Skill Quizzes

We use our diagramming skills to work off of corresponding angles.

- Quiz 1 - QS = 10, PS = 5. Find SR.
- Quiz 2 - William is making a ramp. Find the length of ramp if the height is 6 meters and the base is 36 meters.
- Quiz 3 - We have a right triangle that has a 9 meter height and 18 meter leg. Find the hypotenuse.

### How to Find Missing Sides in a Right Triangle

A right triangle is also known as a right-angled triangle. It is a triangle where one out of the three angles measure 90°.

There are many cases where students must calculate the missing side of these triangles. It is a very useful concept as it is used in many real-life applications, such as calculating the height of buildings, trees, the distance for sailors, and much more. Thanks to a Greek mathematician, Pythagoras, we can easily calculate the dimension of an unknown side of a right triangle when two sides are given. The mathematician devised a relationship between the three sides of a right triangle, which we know as the Pythagorean theorem.

According to the theorem, the sum of the squares of two sides, the perpendicular and the base is equal to the square of the hypotenuse, which is the longest side.

The relationship is given by; (Hypotenuse)^{2} =[(Perpendicular)] ^{2} + [(Base)] ^{2} When you know any two of the three sides, you can, with much ease, find out the unknown side! This worksheet and lesson series with have students find missing lengths of triangles mostly through the help of the Pythagorean theorem.

### How Is This Skill Used in Real Life?

When you are looking to find the length measure of any right triangle-based structure you with refer to using this same math. If you just think about how many different applications of this geometric shape is found in everyday life, you would be amazed. Traditionally contractors are constantly calculating how much sheetrock or wood they need to finish of those right angles. This is something that we see as an obvious application of this skill. Did you ever think about how you could apply this to ladders? If you are leaning the ladder against a wall, it is pitched at a 90 ° angle and this applies to help us understand the length of the ladder or how high it is touching the wall. You can use this in the navigation of all types of vehicles whether on land, sea, or air to find the shortest distance between two Earthly points. Land surveyors have used this technique for decades to help them determine the height of mountains and other terrain. This technique is often applied to astronomy to direct the length of distance between stars and solar systems.