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Unknown Side Lengths in Right Triangle

8.G.B.7
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Aligned To Common Core Standard:

Grade 8 Geometry - 8.G.B.7

How to find Unknown Side Lengths in 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 have to 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.

Printable Worksheets And Lessons






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 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.