Math Problem Statement

Find the missing side lengths in the given special right triangles.

Solution

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Tip:** In a Tip45°-:**45°- In90° triangle, a the hypotenuse45 is always 2\sqrt{2}° times the length of each leg-45.°-90° triangle, the legs are equal, and the hypotenuse is always the leg length multiplied by 2\sqrt{2}.

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Math Problem Analysis

Mathematical Concepts

Special Right Triangles
Radical Simplification
Pythagorean Theorem

Formulas

45°-45°-90° Triangle: Hypotenuse = Leg × √2
30°-60°-90° Triangle: Hypotenuse = 2 × Shorter Leg, Longer Leg = Shorter Leg × √3
Pythagorean Theorem: a² + b² = c²

Theorems

45°-45°-90° Triangle Theorem
30°-60°-90° Triangle Theorem
Pythagorean Theorem

Suitable Grade Level

Grades 8-10