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13. Fill in the missing measurements X 60° 24 30° of the 30-60-90 triangle below. a. x = 12√3; y = 12 b. x = 12; y = 12√3 c. x = 12√2; y = 12 d. x = 12; y = 12√2 A B C D

13. Fill in the missing measurements X 60° 24 30° of the 30-60-90 triangle below. a. x = 12√3; y = 12 b. x = 12; y = 12√3 c. x = 12√2; y = 12 d. x = 12; y = 12√2 A B C D

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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**Question 13: Fill in the missing measurements of the 30-60-90 triangle below.** There is a diagram of a 30-60-90 right triangle. The longer leg opposite the 60° angle is labeled with a length of `24`. The two legs of the triangle are labeled as `x` and `y`, with `x` being the shorter leg opposite the 30° angle, and `y` being the hypotenuse. The angle opposite the shorter leg is `30°`, and the angle opposite the longer leg is `60°`. **Options:** a. \( x = 12\sqrt{3} \); \( y = 12 \) b. \( x = 12 \); \( y = 12\sqrt{3} \) c. \( x = 12\sqrt{2} \); \( y = 12 \) d. \( x = 12 \); \( y = 12\sqrt{2} \) **Bubble Sheet Representation:** There is a bubble sheet next to the question where one can fill in their answer by selecting A, B, C, D, or E. Only bubbles marked A to E are available. **Explanation of Diagrams and Options:** - **30-60-90 Triangle Properties:** - The side ratios of a 30-60-90 triangle are \(1 : \sqrt{3} : 2\), respectively for the side opposite the 30° angle, the side opposite the 60° angle, and the hypotenuse. - Given: - The longer leg (opposite 60°) \( = 24 \) - We need to find: - The shorter leg \( x \) (opposite 30°) - The hypotenuse \( y \) Using the properties: - \( x = \frac{24}{\sqrt{3}} = 8\sqrt{3} \) - \( y = 2 \times 8\sqrt{3} = 24 \) By comparing with the options, check the simplified forms to match: - \( x = 24/\sqrt{3} \) simplifying gives us \( x = 8\sqrt{3} = 12 \) - \( y = 12\sqrt{3} \) So the correct matching option is: - \( b. \) \( x =
Transcribed Image Text:**Question 13: Fill in the missing measurements of the 30-60-90 triangle below.** There is a diagram of a 30-60-90 right triangle. The longer leg opposite the 60° angle is labeled with a length of `24`. The two legs of the triangle are labeled as `x` and `y`, with `x` being the shorter leg opposite the 30° angle, and `y` being the hypotenuse. The angle opposite the shorter leg is `30°`, and the angle opposite the longer leg is `60°`. **Options:** a. \( x = 12\sqrt{3} \); \( y = 12 \) b. \( x = 12 \); \( y = 12\sqrt{3} \) c. \( x = 12\sqrt{2} \); \( y = 12 \) d. \( x = 12 \); \( y = 12\sqrt{2} \) **Bubble Sheet Representation:** There is a bubble sheet next to the question where one can fill in their answer by selecting A, B, C, D, or E. Only bubbles marked A to E are available. **Explanation of Diagrams and Options:** - **30-60-90 Triangle Properties:** - The side ratios of a 30-60-90 triangle are \(1 : \sqrt{3} : 2\), respectively for the side opposite the 30° angle, the side opposite the 60° angle, and the hypotenuse. - Given: - The longer leg (opposite 60°) \( = 24 \) - We need to find: - The shorter leg \( x \) (opposite 30°) - The hypotenuse \( y \) Using the properties: - \( x = \frac{24}{\sqrt{3}} = 8\sqrt{3} \) - \( y = 2 \times 8\sqrt{3} = 24 \) By comparing with the options, check the simplified forms to match: - \( x = 24/\sqrt{3} \) simplifying gives us \( x = 8\sqrt{3} = 12 \) - \( y = 12\sqrt{3} \) So the correct matching option is: - \( b. \) \( x =
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