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Find the missing side lengths. Leave your answ 6) 8 B) 4√3 4√√6 D) 3 45° 60° A) 2√2 C) 16√3 3

Find the missing side lengths. Leave your answ 6) 8 B) 4√3 4√√6 D) 3 45° 60° A) 2√2 C) 16√3 3

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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how would you do 6? (leave in radical)
### Finding the Missing Side Lengths of a Triangle #### Problem Statement: Find the missing side lengths. Leave your answers in simplest radical form. #### Given: A right-angled triangle alongside another right-angled triangle, sharing a common side, is presented. The triangle includes the following details: - One of the sides is 8 units. - The three angles are 45°, 60°, and the right angle (90°). - One of the sides (labeled as \( x \)) is unknown and needs to be found. - Four options are provided for \( x \): #### Options: A) \( \frac{2 \sqrt{2}}{3} \) B) \( \frac{4 \sqrt{3}}{3} \) C) \( \frac{16 \sqrt{3}}{3} \) D) \( \frac{4 \sqrt{6}}{3} \) #### Diagram Description: The diagram shows a right-angled triangle where: - One of the leg lengths is 8 units, positioned as the adjacent side to the 60° angle. - The hypotenuse and other leg lengths remain unknown initially. - The triangle encloses the angles 45°, 60°, and 90°. To solve this problem, it is essential to apply trigonometric ratios and/or the properties of special triangles (30°-60°-90° and 45°-45°-90° triangles) to calculate the unknown side. #### Detailed Steps: 1. Identify the given angles and sides. 2. Use trigonometric identities or properties of known triangle types to determine the lengths. By understanding the trigonometric principles and properties of special right triangles, students can solve for the missing side lengths accurately.
Transcribed Image Text:### Finding the Missing Side Lengths of a Triangle #### Problem Statement: Find the missing side lengths. Leave your answers in simplest radical form. #### Given: A right-angled triangle alongside another right-angled triangle, sharing a common side, is presented. The triangle includes the following details: - One of the sides is 8 units. - The three angles are 45°, 60°, and the right angle (90°). - One of the sides (labeled as \( x \)) is unknown and needs to be found. - Four options are provided for \( x \): #### Options: A) \( \frac{2 \sqrt{2}}{3} \) B) \( \frac{4 \sqrt{3}}{3} \) C) \( \frac{16 \sqrt{3}}{3} \) D) \( \frac{4 \sqrt{6}}{3} \) #### Diagram Description: The diagram shows a right-angled triangle where: - One of the leg lengths is 8 units, positioned as the adjacent side to the 60° angle. - The hypotenuse and other leg lengths remain unknown initially. - The triangle encloses the angles 45°, 60°, and 90°. To solve this problem, it is essential to apply trigonometric ratios and/or the properties of special triangles (30°-60°-90° and 45°-45°-90° triangles) to calculate the unknown side. #### Detailed Steps: 1. Identify the given angles and sides. 2. Use trigonometric identities or properties of known triangle types to determine the lengths. By understanding the trigonometric principles and properties of special right triangles, students can solve for the missing side lengths accurately.
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