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Fun Guide to Special Right Triangles: 45-45-90 and 30-60-90

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Maria Hernandez

7/1/2023

Algebra 2

Special Right Triangles

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Ratios in Right Triangles

Fun Guide to Special Right Triangles: 45-45-90 and 30-60-90

A comprehensive guide to special right triangles 45-45-90 and 30-60-90, focusing on their unique properties and methods for calculating hypotenuse and finding leg lengths in special triangles. The guide covers essential formulas, relationships between sides, and practical applications in geometry.

• Special right triangles follow specific ratio patterns that make calculations more straightforward and predictable
• The 45-45-90 triangle has equal legs and follows the ratio x:x:x√2 for its sides
• The 30-60-90 triangle follows the ratio x:x√3:2x for its sides, where x represents the shortest leg
• Both triangle types are fundamental in geometry and trigonometry applications
• Understanding these patterns enables quick and accurate calculations without complex trigonometric functions

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7/1/2023

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Subjects

Algebra 2

Right Triangles

Ratios in Right Triangles

 

Algebra 2

•

191

•

Jul 1, 2023

•

1 page

Fun Guide to Special Right Triangles: 45-45-90 and 30-60-90

user profile picture

Maria Hernandez

@mariahernandez

A comprehensive guide to special right triangles 45-45-90 and 30-60-90, focusing on their unique properties and methods for calculating hypotenuse and finding leg lengths in special triangles. The guide covers essential formulas, relationships between sides, and practical applications in... Show more

Special Right Triangles 45°-45°-90° leg Ex short leg 45 30-60-70 Ex. 60 45° пур leg X hyp long leg X 45° 30° 45⁰X= 5√2 exact 30⁰ = 2 Short l

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Special Right Triangles: Key Relationships and Calculations

The first page introduces two fundamental special right triangles: the 45-45-90 and 30-60-90 triangles, along with their essential properties and calculations. These triangles have unique characteristics that make them particularly useful in geometric problem-solving.

Definition: A 45-45-90 triangle is a right triangle with two 45-degree angles and one 90-degree angle, where both legs are equal in length.

Highlight: For a 45-45-90 triangle, if the legs are length x, the hypotenuse will always be x√2.

Example: In a 45-45-90 triangle with legs of 5 units, the hypotenuse would be 5√2 ≈ 7.1 units.

Vocabulary: The "leg" refers to either of the two sides that form the right angle in a right triangle, while the "hypotenuse" is the longest side opposite the right angle.

Definition: A 30-60-90 triangle has angles of 30, 60, and 90 degrees, with sides following a specific ratio pattern.

Example: In a 30-60-90 triangle with a short leg of 14 units, the long leg would be 14√3 ≈ 24.2 units, and the hypotenuse would be 28 units.

Highlight: For a 30-60-90 triangle, if the shortest leg is x, then the long leg is x√3, and the hypotenuse is 2x.

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Anna

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

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Marco B

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