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A land surveyor must calculate the distance across a river. KL, in feet. The surveyor measures the distance of JK, KN, and LM. Given that KN is parallel to LM, what is the measure, in feet, of the distance across the river?

A land surveyor must calculate the distance across a river. KL, in feet. The surveyor measures the distance of JK, KN, and LM. Given that KN is parallel to LM, what is the measure, in feet, of the distance across the river?

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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A land surveyor must calculate the distance across a river. KL, in feet. The surveyor measures the distance of JK, KN, and LM. Given that KN is parallel to LM, what is the measure, in feet, of the distance across the river? 

The image shows a list of multiple-choice options, each accompanied by a radio button. The options are as follows: - 25 feet - 32 feet - 40 feet - 65 feet These options are likely part of a question requiring the selection of one answer, commonly used in assessments or quizzes.
Transcribed Image Text:The image shows a list of multiple-choice options, each accompanied by a radio button. The options are as follows: - 25 feet - 32 feet - 40 feet - 65 feet These options are likely part of a question requiring the selection of one answer, commonly used in assessments or quizzes.
The image is a geometric diagram featuring two right triangles that share a common angle at point L. ### Description: 1. **Triangle JLM**: - Right-angled at point L. - **JL** (vertical leg) = 15 feet - **LM** (horizontal leg) = 32 feet - **JM** (hypotenuse) is not labeled with a measurement. 2. **Triangle KLN**: - Also right-angled at point L. - **KL** (vertical leg) is a part of JL in triangle JLM. - **KN** (horizontal leg) = 12 feet - **LN** (part of LM in triangle JLM) is not labeled with a measurement but is parallel to KN. ### Explanation: - Both triangles share side **L** as a common vertex for their right angles. - The larger triangle, **JLM**, uses points J, L, and M to form the triangle. - The segment **KN** in the smaller triangle **KLN** is parallel to the segment of LM from L to N. - **KLN** shares the vertical side **KL** with the larger triangle's vertical side from K to J. By understanding these relationships within the triangles, one can explore concepts such as similarity of triangles and the Pythagorean theorem. This is particularly useful in solving problems involving proportions and distances in right triangles.
Transcribed Image Text:The image is a geometric diagram featuring two right triangles that share a common angle at point L. ### Description: 1. **Triangle JLM**: - Right-angled at point L. - **JL** (vertical leg) = 15 feet - **LM** (horizontal leg) = 32 feet - **JM** (hypotenuse) is not labeled with a measurement. 2. **Triangle KLN**: - Also right-angled at point L. - **KL** (vertical leg) is a part of JL in triangle JLM. - **KN** (horizontal leg) = 12 feet - **LN** (part of LM in triangle JLM) is not labeled with a measurement but is parallel to KN. ### Explanation: - Both triangles share side **L** as a common vertex for their right angles. - The larger triangle, **JLM**, uses points J, L, and M to form the triangle. - The segment **KN** in the smaller triangle **KLN** is parallel to the segment of LM from L to N. - **KLN** shares the vertical side **KL** with the larger triangle's vertical side from K to J. By understanding these relationships within the triangles, one can explore concepts such as similarity of triangles and the Pythagorean theorem. This is particularly useful in solving problems involving proportions and distances in right triangles.
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