Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees. Is this a safe ramp? Explain or show your reasoning. * 20 100
Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees. Is this a safe ramp? Explain or show your reasoning. * 20 100
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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![Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees. Is this a safe ramp? Explain or show your reasoning.
### Diagram Explanation
The diagram shows a right triangle representing a ramp with a car on it. The horizontal side (base) of the triangle is labeled as 100 units, and the vertical side (height) is labeled as 20 units. The car is positioned on the hypotenuse, which represents the ramp.
To determine if this ramp is safe:
1. **Calculate the angle of incline** using the tangent function:
\[
\text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{100} = 0.2
\]
2. **Find the angle**:
\[
\theta = \text{tan}^{-1}(0.2) \approx 11.31 \text{ degrees}
\]
Since the calculated angle of approximately 11.31 degrees is greater than the maximum safe incline of 8.5 degrees, this ramp is not safe.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7ac2d3e-09ac-4a40-9e8f-1af7c3ce9166%2Ff8343b40-b0a3-40bb-8a28-d5a24e558369%2Fxvh8bqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees. Is this a safe ramp? Explain or show your reasoning.
### Diagram Explanation
The diagram shows a right triangle representing a ramp with a car on it. The horizontal side (base) of the triangle is labeled as 100 units, and the vertical side (height) is labeled as 20 units. The car is positioned on the hypotenuse, which represents the ramp.
To determine if this ramp is safe:
1. **Calculate the angle of incline** using the tangent function:
\[
\text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{100} = 0.2
\]
2. **Find the angle**:
\[
\theta = \text{tan}^{-1}(0.2) \approx 11.31 \text{ degrees}
\]
Since the calculated angle of approximately 11.31 degrees is greater than the maximum safe incline of 8.5 degrees, this ramp is not safe.
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