LESSON:       Slope and Pythagorean Theorem.....Click Here to Download File

ACTIVITY: Designing a Wheelchair Ramp

PURPOSE OF THIS ACTIVITY:  To design a wheelchair ramp for a given location.  Scale drawings will be used to show the placement of the ramp.  The Pythagorean Theorem will be used to find the dimensions of the ramp.  The steepness of the ramp will be expressed as a ratio, and an angle.

HYPOTHESIS:  Consider the following situation.  There are three steps that lead from the dining room down to the family room.  A wheelchair ramp needs to be constructed from the family room up to the dining room.  To the best of your ability estimate the following measurements.

Vertical Height of the Ramp ( cm )

30   40   50   60   70

Horizontal Length of the Ramp ( m )

3   4   5   6   7

Slant Height of the Ramp

3.5   4.5   5.5   6.5   7.5

Steepness of the Ramp;    height : length

1 : 4   1: 6   1 : 8   1 : 10   1 : 12   1 : 14

PART ONE:    How Steep is Steep:

To determine an appropriate incline for a wheelchair ramp

THE PROBLEM:        

?Who can negotiate the steepest wheelchair ramp?

?Set up ramp

?Use the data chart to record the appropriate dimensions

?Use a wheelchair to negotiate the ramp and make note the difficulty

?Adjust the height of the ramp and repeat                     

COMPLETE THE DATA CHART

?Record the name of the student riding the wheelchair

?Measure and record the slant height of the ramp

?Measure and record the rise - i.e.. the vertical height

?Use the Pythagorean Theorem to calculate the run - i.e.. the horizontal length

?NOTE:    i.     Pythagorean Theorem:  h2 = a2 + b2

ii.   the TI-83+ may be used to complete column four

?Calculate the steepness of the ramp and express it in the appropriate format

                        ratio:    1 :                    angle:   = tan-1(slope)

CONCLUSION:         What is a reasonable incline for a wheelchair ramp?

EXERCISE ONE:          Slope and the Pythagorean Theorem

Use the given information to complete the following data chart. 

Show some of your work at the bottom of the page.

SHOW SOME OF THE CALCULATIONS

PART  TWO:  Designing the Wheelchair Ramp

PURPOSE:  To design a wheelchair ramp to fit a given location.          

THE PROBLEM:  Identify an location in the school that requires a wheelchair ramp to allow all students access to this area. Design a ramp to fit the  stairway leading to this part of the school.

THE SOLUTION: 

?describe the location for the wheelchair ramp

?measure the area

?decide and calculate the appropriate measurements for the ramp

?make a scale drawing of the ramp and a scale drawing of the area with the ramp in place

?conclusion;  Will a wheelchair ramp in this location be appropriate?  Discuss the advantages and the disadvantages.

?extension;        i.          Investigate any other aspect of this ramp that may not have been taken into account.

                          ii.          Determine the amount of material required and the approximate cost of building this wheelchair ramp.        

EXERCISE TWO:  Pythagorean Theorem and Steepness

1.         Use the Pythagorean Theorem to find the value of the unknown side. Find the    steepness of the hypotenuse in relation to the other two sides.

            a)

            b)

            c)        

 steepness = 2 : 3

2.         Use the information given in the diagram to find the values of  x  and  y, and

            the steepness of the slant height.

3.         Find the length of the line from the bottom right corner of the box to the top left corner of the box.  The box measures  3 m by  4 m by  12 m.

4.         Find the altitude of an equilateral triangle it the length of each side is  18 cm

QUIZ                                                   NAME: ____________________________

1.         The diagram represents the three steps to the             front door of a building.  The riser height             is 18 cm and the tread depth is 26 cm.             Design a ramp that will allow wheelchair             access to this building.             a)         Calculate the length and the slope of your ramp.             b)         The builder constructed a ramp 5.5 m long.  Will                         this ramp be acceptable? Discuss.

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