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i app.edulastic. Dulce's Folder Bell Schedules - A... Biology KAREN 4TH HBUHSD E- Question 35/36 NEXT BOOKM. Bookmar 35 Solve for x. 60° 3V3 A 9 B 9v2 C 6V3 D 9V3

i app.edulastic. Dulce's Folder Bell Schedules - A... Biology KAREN 4TH HBUHSD E- Question 35/36 NEXT BOOKM. Bookmar 35 Solve for x. 60° 3V3 A 9 B 9v2 C 6V3 D 9V3

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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35. Solve for x.
### Trigonometry Problem: Solve for x In this problem, we are given a right triangle with the following parameters: - One angle is 60° - The length of the side opposite the 60° angle is \(3\sqrt{3}\) - We need to solve for the length of the hypotenuse \(x\) #### Given: - Angle \( \theta = 60° \) - Opposite side to angle \( \theta \): \( 3\sqrt{3} \) - Right angle #### Options: A. \( 9 \) B. \( 9\sqrt{2} \) C. \( 6\sqrt{3} \) D. \( 9\sqrt{3} \) #### Solution: To solve for \( x \), we can use the relationship between the sides of a 30°-60°-90° triangle. In a 30°-60°-90° triangle: - The length of the hypotenuse is twice the length of the shorter leg (opposite the 30° angle). - The length of the longer leg (opposite the 60° angle) is \( \sqrt{3} \) times the length of the shorter leg. Given that the length of the longer leg is \( 3\sqrt{3} \): - Let the shorter leg be \( y \). - Therefore, \( y \cdot \sqrt{3} = 3\sqrt{3} \) - Solving for \( y \): \( y = 3 \) - The hypotenuse \( x \) is twice the length of the shorter leg: - \( x = 2 \cdot y \) - Thus, \( x = 2 \cdot 3 = 6 \) #### Correct Answer: C. \( 6\sqrt{3} \) However, since none of the options directly align with this solution, it might be necessary for a reevaluation, or there may have been a different approach expected in the configuration of this problem that needs a more detailed insight.
Transcribed Image Text:### Trigonometry Problem: Solve for x In this problem, we are given a right triangle with the following parameters: - One angle is 60° - The length of the side opposite the 60° angle is \(3\sqrt{3}\) - We need to solve for the length of the hypotenuse \(x\) #### Given: - Angle \( \theta = 60° \) - Opposite side to angle \( \theta \): \( 3\sqrt{3} \) - Right angle #### Options: A. \( 9 \) B. \( 9\sqrt{2} \) C. \( 6\sqrt{3} \) D. \( 9\sqrt{3} \) #### Solution: To solve for \( x \), we can use the relationship between the sides of a 30°-60°-90° triangle. In a 30°-60°-90° triangle: - The length of the hypotenuse is twice the length of the shorter leg (opposite the 30° angle). - The length of the longer leg (opposite the 60° angle) is \( \sqrt{3} \) times the length of the shorter leg. Given that the length of the longer leg is \( 3\sqrt{3} \): - Let the shorter leg be \( y \). - Therefore, \( y \cdot \sqrt{3} = 3\sqrt{3} \) - Solving for \( y \): \( y = 3 \) - The hypotenuse \( x \) is twice the length of the shorter leg: - \( x = 2 \cdot y \) - Thus, \( x = 2 \cdot 3 = 6 \) #### Correct Answer: C. \( 6\sqrt{3} \) However, since none of the options directly align with this solution, it might be necessary for a reevaluation, or there may have been a different approach expected in the configuration of this problem that needs a more detailed insight.
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