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Hans is constructing an accessibility ramp for a library that should reach a height of 27cm with an angle no greater than 13 degrees 

 

a) Find the shortest possibe length of ramp to achieve this.

 

b) Hans cuts a length of wood to make the ramp. He cuts it to the length calculated in part (a) but can only cut it with an accuracy to the nearest centimetre. if the actual height required by the ramp is 27.43cm, find the maximum possible percentage error between the desired 13 degrees and the actual angle of the ramp.

 Jul 16, 2019
 #1
avatar+103999 
+1

Here's the "a" part

 

sin (13°)  =  27 /  Ramp Length            rearrange as

 

Ramp Length  =    27  /  sin (13°)   ≈   120.03  cm

 

 

cool cool cool

 Jul 16, 2019
edited by CPhill  Jul 16, 2019
 #2
avatar+103999 
+1

Here's my attepmt at part "b"

 

To the nearst cm.....the ramp length  is 120cm

 

So....the angle,  θ, in this case  can be found as

 

sin   θ =    27.43  / 120

 

To find   θ  use the arcsin  function

 

arcsin ( 27.43 / 120 )  =   θ ≈  13.21°

 

Percentage error  =    [ 13.21  - 13 ]  / 13    ≈ .016  =  1.6%

 

 

cool cool cool

 Jul 16, 2019

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