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In the diagram of the right triangle ADE below, BE || DE. Which ratio is always equivalent to the sine of B? ВС BC AB Submit Answer AC AÇ AD AC AB

In the diagram of the right triangle ADE below, BE || DE. Which ratio is always equivalent to the sine of B? ВС BC AB Submit Answer AC AÇ AD AC AB

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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**Mathematics - Trigonometry Learning Module** **Understanding Trigonometric Ratios** **Problem Statement:** In the diagram of the right triangle ADE below, BE ∥ DE. Which ratio is always equivalent to the sine of angle B? **Diagram and Explanation:** The provided diagram depicts triangle ADE with a right angle at E. In the diagram: - Point A is at the leftmost end. - Point D is at the top of the triangle. - Point E is at the bottom right, forming a right angle (90°) with DE. - Point B lies on the hypotenuse AD, forming triangle ABC. - BE is parallel to DE. **Question:** Which of the given ratios is equivalent to the sine of angle B? **Answer Options:** - BC / AC - BC / AB - AC / AD - AC / AB **Diagram Analysis:** The diagram showcases triangle ADE with an additional partition creating triangle ABC within it. Since BE ∥ DE, triangles ADE and ABC are similar, which implies that the trigonometric ratios for angle B in triangle ADE can also be evaluated in triangle ABC. **Submit Answer Button:** - After selecting the appropriate ratio, click on "Submit Answer" to check your response. Understanding and practicing the relationships and ratios in similar triangles will help in mastering trigonometric functions and their applications.
Transcribed Image Text:**Mathematics - Trigonometry Learning Module** **Understanding Trigonometric Ratios** **Problem Statement:** In the diagram of the right triangle ADE below, BE ∥ DE. Which ratio is always equivalent to the sine of angle B? **Diagram and Explanation:** The provided diagram depicts triangle ADE with a right angle at E. In the diagram: - Point A is at the leftmost end. - Point D is at the top of the triangle. - Point E is at the bottom right, forming a right angle (90°) with DE. - Point B lies on the hypotenuse AD, forming triangle ABC. - BE is parallel to DE. **Question:** Which of the given ratios is equivalent to the sine of angle B? **Answer Options:** - BC / AC - BC / AB - AC / AD - AC / AB **Diagram Analysis:** The diagram showcases triangle ADE with an additional partition creating triangle ABC within it. Since BE ∥ DE, triangles ADE and ABC are similar, which implies that the trigonometric ratios for angle B in triangle ADE can also be evaluated in triangle ABC. **Submit Answer Button:** - After selecting the appropriate ratio, click on "Submit Answer" to check your response. Understanding and practicing the relationships and ratios in similar triangles will help in mastering trigonometric functions and their applications.
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