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Determine the type of triangle that is formed given the set of side length measurements below: 5, 5, 5√2 Type of triangle: 8, 16, 8√3 Type of triangle: 2x 60° 45 $√2 JA 30⁰ 45⁰ S x√3 Special Right Triangles

Determine the type of triangle that is formed given the set of side length measurements below: 5, 5, 5√2 Type of triangle: 8, 16, 8√3 Type of triangle: 2x 60° 45 $√2 JA 30⁰ 45⁰ S x√3 Special Right Triangles

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Determine the Type of Triangle Based on Side Lengths** Given the set of side length measurements below, identify the type of triangle: 1. **Side lengths:** 5, 5, \(5\sqrt{2}\) - **Type of triangle:** [Dropdown] 2. **Side lengths:** 8, 16, \(8\sqrt{3}\) - **Type of triangle:** [Dropdown] ### Special Right Triangles Diagram Below the text, there is a diagram showing two special right triangles: 1. **First Triangle (30°-60°-90° Triangle):** - One angle is 30°, another is 60°, and the right angle (90°). - Side opposite the 30° angle is labeled \(x\). - Side opposite the 60° angle is labeled \(x\sqrt{3}\). - Hypotenuse (the side opposite the 90° angle) is labeled \(2x\). 2. **Second Triangle (45°-45°-90° Triangle):** - Both non-right angles are 45° each. - Both legs (sides opposite the 45° angles) are labeled \(s\). - Hypotenuse (the side opposite the 90° angle) is labeled \(s\sqrt{2}\). Both triangles are specifically categorized as "Special Right Triangles." This content is designed to help students identify types of triangles based on given side lengths and to recognize the properties of special right triangles, such as 30°-60°-90° and 45°-45°-90° triangles.
Transcribed Image Text:**Determine the Type of Triangle Based on Side Lengths** Given the set of side length measurements below, identify the type of triangle: 1. **Side lengths:** 5, 5, \(5\sqrt{2}\) - **Type of triangle:** [Dropdown] 2. **Side lengths:** 8, 16, \(8\sqrt{3}\) - **Type of triangle:** [Dropdown] ### Special Right Triangles Diagram Below the text, there is a diagram showing two special right triangles: 1. **First Triangle (30°-60°-90° Triangle):** - One angle is 30°, another is 60°, and the right angle (90°). - Side opposite the 30° angle is labeled \(x\). - Side opposite the 60° angle is labeled \(x\sqrt{3}\). - Hypotenuse (the side opposite the 90° angle) is labeled \(2x\). 2. **Second Triangle (45°-45°-90° Triangle):** - Both non-right angles are 45° each. - Both legs (sides opposite the 45° angles) are labeled \(s\). - Hypotenuse (the side opposite the 90° angle) is labeled \(s\sqrt{2}\). Both triangles are specifically categorized as "Special Right Triangles." This content is designed to help students identify types of triangles based on given side lengths and to recognize the properties of special right triangles, such as 30°-60°-90° and 45°-45°-90° triangles.
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