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16* A surveyor sees a building across the river. Standing at point A he measures the angle of ele- vation from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again measures the angle of elevation and finds it to be 15°. (See Figure 12.26.) Assuming that it makes a 90-degree angle with the floor, approximately how tall is the building? B 15° 100 A 30° river Figure 12.26 building

16* A surveyor sees a building across the river. Standing at point A he measures the angle of ele- vation from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again measures the angle of elevation and finds it to be 15°. (See Figure 12.26.) Assuming that it makes a 90-degree angle with the floor, approximately how tall is the building? B 15° 100 A 30° river Figure 12.26 building

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 surveyor sees a building across the river. Standing at point A, he measures the angle of elevation from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again measures the angle of elevation and finds it to be 15 degrees. (See Figure 12.26.) Assuming that it makes a 90-degree angle with the floor, approximately how tall is the building? **Figure 12.26 Description:** The figure illustrates a diagram showing the scenario described in the problem. Point B is located 100 feet behind point A on the same horizontal line. From both points, lines are drawn to the top of the building across the river, forming two right triangles. - Triangle at point A: - Angle of elevation is 30 degrees. - The building creates a vertical line perpendicular to the riverbank, forming a right angle with the ground. - Triangle from point B: - Angle of elevation is 15 degrees. - The distance from A to B is 100 feet along the horizontal. The objective is to calculate the height of the building using the given angles and horizontal distance.
Transcribed Image Text:A surveyor sees a building across the river. Standing at point A, he measures the angle of elevation from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again measures the angle of elevation and finds it to be 15 degrees. (See Figure 12.26.) Assuming that it makes a 90-degree angle with the floor, approximately how tall is the building? **Figure 12.26 Description:** The figure illustrates a diagram showing the scenario described in the problem. Point B is located 100 feet behind point A on the same horizontal line. From both points, lines are drawn to the top of the building across the river, forming two right triangles. - Triangle at point A: - Angle of elevation is 30 degrees. - The building creates a vertical line perpendicular to the riverbank, forming a right angle with the ground. - Triangle from point B: - Angle of elevation is 15 degrees. - The distance from A to B is 100 feet along the horizontal. The objective is to calculate the height of the building using the given angles and horizontal distance.
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