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17) 18) 17. x = y y y = 45° 6V2 4V3 30° 18. x = y = 19. u = 19) 20) 6 y = 45 3V3 u 60° 20. m = m n =

17) 18) 17. x = y y y = 45° 6V2 4V3 30° 18. x = y = 19. u = 19) 20) 6 y = 45 3V3 u 60° 20. m = m n =

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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### Triangles and Trigonometry Problems **Problem Descriptions:** **17) Triangle:** - A right triangle with: - One angle measuring \(30^\circ\). - The side opposite the \(30^\circ\) angle is labeled \(4\sqrt{3}\). - Hypotenuse is labeled \(y\). - Other leg is labeled \(x\). **18) Triangle:** - A right triangle with: - One angle measuring \(45^\circ\). - Hypotenuse labeled as \(6\sqrt{2}\). - Legs labeled \(x\) and \(y\). **19) Triangle:** - A right triangle with: - One angle measuring \(45^\circ\). - Side adjacent to the \(45^\circ\) angle labeled \(3\sqrt{3}\). - Legs labeled \(u\) and \(v\). **20) Triangle:** - A right triangle with: - One angle measuring \(60^\circ\). - Opposite side to the \(60^\circ\) angle labeled as \(6\). - Other leg labeled \(n\). - Hypotenuse labeled \(m\). **Equations for Solutions:** Fill in the missing sides for each triangle using trigonometric ratios or special right triangle properties. - **17)** \(x = \_\_\_\_\_\_\_\_\_\) \(y = \_\_\_\_\_\_\_\_\_\) - **18)** \(x = \_\_\_\_\_\_\_\_\_\) \(y = \_\_\_\_\_\_\_\_\_\) - **19)** \(u = \_\_\_\_\_\_\_\_\_\) \(v = \_\_\_\_\_\_\_\_\_\) - **20)** \(m = \_\_\_\_\_\_\_\_\_\) \(n = \_\_\_\_\_\_\_\_\_\) **Instructions:** - Calculate the missing side lengths using the properties of right triangles. - Use known trigonometric identities and values for \(30^\circ\), \(45^\circ\), and \(60^\circ\) angles.
Transcribed Image Text:### Triangles and Trigonometry Problems **Problem Descriptions:** **17) Triangle:** - A right triangle with: - One angle measuring \(30^\circ\). - The side opposite the \(30^\circ\) angle is labeled \(4\sqrt{3}\). - Hypotenuse is labeled \(y\). - Other leg is labeled \(x\). **18) Triangle:** - A right triangle with: - One angle measuring \(45^\circ\). - Hypotenuse labeled as \(6\sqrt{2}\). - Legs labeled \(x\) and \(y\). **19) Triangle:** - A right triangle with: - One angle measuring \(45^\circ\). - Side adjacent to the \(45^\circ\) angle labeled \(3\sqrt{3}\). - Legs labeled \(u\) and \(v\). **20) Triangle:** - A right triangle with: - One angle measuring \(60^\circ\). - Opposite side to the \(60^\circ\) angle labeled as \(6\). - Other leg labeled \(n\). - Hypotenuse labeled \(m\). **Equations for Solutions:** Fill in the missing sides for each triangle using trigonometric ratios or special right triangle properties. - **17)** \(x = \_\_\_\_\_\_\_\_\_\) \(y = \_\_\_\_\_\_\_\_\_\) - **18)** \(x = \_\_\_\_\_\_\_\_\_\) \(y = \_\_\_\_\_\_\_\_\_\) - **19)** \(u = \_\_\_\_\_\_\_\_\_\) \(v = \_\_\_\_\_\_\_\_\_\) - **20)** \(m = \_\_\_\_\_\_\_\_\_\) \(n = \_\_\_\_\_\_\_\_\_\) **Instructions:** - Calculate the missing side lengths using the properties of right triangles. - Use known trigonometric identities and values for \(30^\circ\), \(45^\circ\), and \(60^\circ\) angles.
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