Notes 8.2 Part 1
45-45-90 Triangles
Objective: To use 45-45-90 triangle properties to solve for
missing side lengths.
Label what you know about a 45-45-90 triangle.
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Notes on Solving for Missing Side Lengths in 45-45-90 Triangles, Study notes of Advanced Calculus
These notes provide instructions for identifying and solving for missing side lengths in 45-45-90 triangles using the given triangle properties. Students are encouraged to work in groups and apply the Pythagorean theorem to find the lengths of the hypotenuse and legs, and to observe the relationship between the sides. A formula for finding the lengths of the sides is also provided.
What you will learn
- What is the formula for finding the lengths of the sides of a 45-45-90 triangle?
- What is the relationship between the lengths of the legs and the hypotenuse in a 45-45-90 triangle?
- How can you use the Pythagorean theorem to find the lengths of the sides in a 45-45-90 triangle?
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2021/2022
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Notes 8.2 Part 1
45-45-90 Triangles
Objective: To use 45-45-90 triangle properties to solve for missing side lengths. Label what you know about a 45-45-90 triangle.
Get into groups of 2 or 3 and complete the following:
- Sketch four isosceles right triangles (45-45-90).
- Pick four different whole numbers for the lengths of the legs of each triangle.
- Use the Pythagorean Theorem to find the lengths of the hypotenuse of each triangle. (If you do not get a whole number as your answer, leave it in simplified radical form.)
- Do you see a pattern or relationship between the lengths of the legs and the hypotenuse of in these triangles?
- Write a formula for finding the lengths of the sides of a 45-45-90 triangle, based upon what you came up with in step 4.
What is the length of the hypotenuse of a 45-45-90 triangle with leg length 5√3? The length of the hypotenuse of a 45-45-90 triangle is 10. What is the length of one leg?
Extra Practice Problems