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# Right Triangle Trigonometry

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An architect is designing a ramp that allows handicapped persons to get to a door's level that is 12 feet off the ground.  The ramp cannot have an incline surpassing a ratio of 1:12.  What is the maximum angle of elevation for the ramp rounded to the nearest hundredth of a degree?  What is the shortest possible lenght of the ramp, rounded to the nearest tenth of a foot?

I know you should use Pythagorean Theorem for this, but I am not sure where to start.

Mar 23, 2019
edited by ladybug1031  Mar 23, 2019

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I think that you might need physics for this, as the answers for each is 90 degress and 12 feet. I am possibly incorrect, but this question's wording does not make sense.

Hoping this helped,

asdf334

Mar 23, 2019
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I have edited the question to correct spelling and added clarification.  We are studying Right Angle Trigonometry.

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To have the shortest possible and maximum angle of elevation, we want the incline to have the maximum ratio, 12:1. So, we know that it is a right triangle with base 1 and height 12. So, our answers are tan^-1(12) and sqrt145.

Hoping this helped, asdf334

Mar 23, 2019
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I think that you might need physics for this, as the answers for each is 90 degress and 12 feet. I am possibly incorrect, but this question's wording does not make sense.

asdf335

To have the shortest possible and maximum angle of elevation, we want the incline to have the maximum ratio, 12:1. So, we know that it is a right triangle with base 1 and height 12. So, our answers are tan^-1(12) and sqrt145. – asdf335

You do not need physics to solve this; however, you may need a physic (laxative) to purge yourself of the bullshit that’s impeding your access to the trigonometry needed for solving it.

$$\text{Ramp angle } = \arctan (\dfrac{1}{12}) \approx 4.8°\\ \text{Ramp length } = \dfrac{12}{sin (4.76°)} \approx 144.6 ft$$

You are hopping this helps, but I’m sure the gimps of world are hoping you do not pursue a career in architecture.

GA

Mar 24, 2019