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9) A 30-foot long support wire for a 16 foot-high streetlight runs from the top corner of a building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the street light is 6 feet. How tall is the building? F. 16 ft. G. 20 ft. H. 32 ft. I. 48 ft. Work: ||||||||||

9) A 30-foot long support wire for a 16 foot-high streetlight runs from the top corner of a building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the street light is 6 feet. How tall is the building? F. 16 ft. G. 20 ft. H. 32 ft. I. 48 ft. Work: ||||||||||

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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### Problem 9: A 30-foot long support wire for a 16-foot-high streetlight runs from the top corner of a building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the streetlight is 6 feet. How tall is the building? **Options:** - F. 16 ft. - G. 20 ft. - H. 32 ft. - I. 48 ft. **Explanation Diagram:** The diagram shows a right triangle formed by the building, the ground, and the support wire. The streetlight is part of the vertical side, with a height of 16 feet. The wire is the hypotenuse of the triangle, measuring 30 feet. A segment of 6 feet from the top of the building to the top of the streetlight is indicated. **Calculation:** To find the height of the building, you need to determine the vertical distance from the ground to the top of the building, using the Pythagorean theorem if necessary. ### Problem 10: Given \( \overline{DE} \parallel \overline{BC} \), which proportion is justified by the image below? **Options:** - A. \( \frac{18}{24} = \frac{24}{8} \) - B. \( \frac{18}{6} = \frac{8}{24} \) - C. \( \frac{18}{24} = \frac{24}{32} \) - D. \( \frac{18}{6} = \frac{8}{24} \) **Diagram Explanation:** The diagram consists of a triangle \( \triangle ABC \) with line segment \( \overline{DE} \) parallel to base \( \overline{BC} \). The segments are labeled with their respective lengths: \( AD = 18 \), \( DE = 24 \), \( DC = 6 \), and \( CB = 8 \). **Mathematical Justification:** To find the correct proportion, use the properties of similar triangles. The segments create two smaller, similar triangles: \( \triangle ADE \) and \( \triangle ABC \). Use corresponding sides to establish the correct proportion.
Transcribed Image Text:### Problem 9: A 30-foot long support wire for a 16-foot-high streetlight runs from the top corner of a building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the streetlight is 6 feet. How tall is the building? **Options:** - F. 16 ft. - G. 20 ft. - H. 32 ft. - I. 48 ft. **Explanation Diagram:** The diagram shows a right triangle formed by the building, the ground, and the support wire. The streetlight is part of the vertical side, with a height of 16 feet. The wire is the hypotenuse of the triangle, measuring 30 feet. A segment of 6 feet from the top of the building to the top of the streetlight is indicated. **Calculation:** To find the height of the building, you need to determine the vertical distance from the ground to the top of the building, using the Pythagorean theorem if necessary. ### Problem 10: Given \( \overline{DE} \parallel \overline{BC} \), which proportion is justified by the image below? **Options:** - A. \( \frac{18}{24} = \frac{24}{8} \) - B. \( \frac{18}{6} = \frac{8}{24} \) - C. \( \frac{18}{24} = \frac{24}{32} \) - D. \( \frac{18}{6} = \frac{8}{24} \) **Diagram Explanation:** The diagram consists of a triangle \( \triangle ABC \) with line segment \( \overline{DE} \) parallel to base \( \overline{BC} \). The segments are labeled with their respective lengths: \( AD = 18 \), \( DE = 24 \), \( DC = 6 \), and \( CB = 8 \). **Mathematical Justification:** To find the correct proportion, use the properties of similar triangles. The segments create two smaller, similar triangles: \( \triangle ADE \) and \( \triangle ABC \). Use corresponding sides to establish the correct proportion.
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