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Geometry problem demonstrating the properties of a 30-60-90 triangle with side ratios and calculations.

A diagram of a 30-60-90 right triangle with side lengths labeled, including calculations for x and y, from a KutaSoftware Geometry lesson on special right triangles.

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Show Answer Key & Explanations Step-by-step solution for: KutaSoftware: Geometry- Special Right Triangles Part 2 - YouTube

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- The triangle is a 30°-60°-90° special right triangle.
- In a 30°-60°-90° triangle, the sides are in the ratio 1 : √3 : 2, where:
- The side opposite the 30° angle is the shortest leg (let’s call it z).
- The side opposite the 60° angle is the longer leg (√3 * z).
- The hypotenuse is twice the shortest leg (2z).
- The hypotenuse is given as 16, so: 2z = 16 → z = 8.
- The side opposite the 60° angle (x) is the longer leg: x = √3 * z = √3 * 8 = 8√3.
- The side opposite the 30° angle (y) is the shortest leg: y = z = 8.

Parent Tip: Review the logic above to help your child master the concept of special right triangles geometry worksheet.

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