LESSON:       Steepness and the Pythagorean Theorem.....Click Here to Download File

ACTIVITY: Designing a Skateboard Ramp

PURPOSE OF THIS ACTIVITY:  To design a skateboard 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, a percent,  an angle and as slope.

HYPOTHESIS:  Consider the following situation.  From the pathway there are  four steps that take you from ground level to a raised patio.  A skateboard ramp needs to be constructed to allow skaters easy access from the pathway up to the patio. To the best of your ability estimate the following measurements.

Vertical Height of the Ramp ( cm )

50   60   70   80   90   100   120

Horizontal Length of the Ramp ( m )

3   4   5   6   7   8   9

Slant Height of the Ramp ( m )

3.5   4.5   5.5   6.5   7.5   8.5   9.5 

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 the skateboard ramp

THE PROBLEM:        

?Who can ride up the steepest skateboard ramp?

?Set up ramp

?Use the data chart to record the appropriate dimensions

?Use a skateboard to ride up the ramp and make note the difficulty

?Adjust the height of the ramp and repeat   NOTE: use a spotter for safety                   

COMPLETE THE DATA CHART

?Record the name of the skater

?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    

percent       % =   100

ratio           rise : run = 1 :

angle          = tan-1()

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

EXERCISE ONE:          Steepness 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 Skateboard Ramp

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

THE PROBLEM:         Pick a location around the school that would require a skateboard ramp that would allow a skater to ride up the ramp to an elevated platform

THE SOLUTION: 

?describe the location for the skateboard 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.  Express the steepness in two different ways.

            a)

b)

            c)        

slope = 2

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

            Find the steepness of the ramp.

3.         Find the length of the diagonal of the box measuring 3 m by 2 m by 2.5 m.

4.         Mike is flying a kite using a 30 m string.  The height of the kite 16 m.  If a weighted marker is dropped from the kite, how far from Mike will the marker hit the ground?

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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