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An architect designs a wheelchair ramp for a historical building. The entry way is a level platform at the top of stairs that are 3 meters above ground level and extend 4 m out from the building. There is an obstacle 25 m from the stairs, and the city code for ramps limits the incline angle to 6º. Is there sufficient distance for a ramp within this limit? How do you know? O Yes, because the ratio of O No, because the ratio of O No, because the ratio of is less than tan 6º. is greater than sin 6º. is greater than tan 6º. O Yes, because the ratio of is less than sin 6º.

An architect designs a wheelchair ramp for a historical building. The entry way is a level platform at the top of stairs that are 3 meters above ground level and extend 4 m out from the building. There is an obstacle 25 m from the stairs, and the city code for ramps limits the incline angle to 6º. Is there sufficient distance for a ramp within this limit? How do you know? O Yes, because the ratio of O No, because the ratio of O No, because the ratio of is less than tan 6º. is greater than sin 6º. is greater than tan 6º. O Yes, because the ratio of is less than sin 6º.

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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**Wheelchair Ramp Design Problem** *Background Information:* An architect designs a wheelchair ramp for a historical building. The entryway is a level platform at the top of stairs that are 3 meters above ground level and extend 4 meters out from the building. There is an obstacle 25 meters from the stairs, and the city code for ramps limits the incline angle to 6°. *Question:* Is there sufficient distance for a ramp within this limit? How do you know? *Options:* 1. ○ Yes, because the ratio of \(\dfrac{4}{25}\) is less than \(\tan 6°\). 2. ○ No, because the ratio of \(\dfrac{4}{25}\) is greater than \(\sin 6°\). 3. ○ No, because the ratio of \(\dfrac{3}{25}\) is greater than \(\tan 6°\). 4. ○ Yes, because the ratio of \(\dfrac{3}{25}\) is less than \(\sin 6°\). *Explanation:* You need to determine whether the proposed ramp fits within the spatial and angular constraints dictated by the city code. The key comparison involves the ratio of the height to the length of the ramp compared to the trigonometric values for a 6° angle.
Transcribed Image Text:**Wheelchair Ramp Design Problem** *Background Information:* An architect designs a wheelchair ramp for a historical building. The entryway is a level platform at the top of stairs that are 3 meters above ground level and extend 4 meters out from the building. There is an obstacle 25 meters from the stairs, and the city code for ramps limits the incline angle to 6°. *Question:* Is there sufficient distance for a ramp within this limit? How do you know? *Options:* 1. ○ Yes, because the ratio of \(\dfrac{4}{25}\) is less than \(\tan 6°\). 2. ○ No, because the ratio of \(\dfrac{4}{25}\) is greater than \(\sin 6°\). 3. ○ No, because the ratio of \(\dfrac{3}{25}\) is greater than \(\tan 6°\). 4. ○ Yes, because the ratio of \(\dfrac{3}{25}\) is less than \(\sin 6°\). *Explanation:* You need to determine whether the proposed ramp fits within the spatial and angular constraints dictated by the city code. The key comparison involves the ratio of the height to the length of the ramp compared to the trigonometric values for a 6° angle.
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