Always give answers to 2 decimal places.  
 
 
 
  Q1)  
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
 
  Calculate the missing side given the other two:  
 
    a b c  
  a) 3 4  
  b) 2 5  
  c) 1 7  
  d) 3 16  
  e) 8 26  
  f) 1 32  
  g) 6 20  
  h) 8 10  
  i) 12 40  
 
  Q2)
 
   
   
   
   
   
   
   
   
   
   
   
  Calculagte the length of the diagonal blue line inside the cuboid:
 
  Q3) Lewis and Sebastian live in the same apartment block.
  Lewis walks due south to work and Sebastian walks due East.
  They both leave the apartment block at the same time.
  When Lewis is 5 miles south of the apartment, the two friends are
  1 mile further apart than Sebastian's distance from the apartment.
  How far is Sebastian from the apartment?
  (Hint: let x be Sebastian's distance from the apartment, solve for x.)
 
  x =  
 
   
 
 
   
 
 
 
   
 
  Determine the side lengths of the blue triangle:  
 
  x =  
  y =  
  z =  
 
  Do you think that the blue triangle is in fact right angled? Why?  
 
   
   
 
  Q5) Challenge question for the adventurous!  
 
  You're stood on the beach looking out to sea.  
  You watch a ship sailing away over the horizon.  
  But, how far away is the horizon?  
 
  Assume that the radius of the earth is 6378100 metres and you are 1.7m tall.
  For these values, how far is the horizon to the nearest metre? m
   
 
  You can use this calculator to find the distance to the horizon (in miles)  
  from a chosen height (in metres):  
 
  Height in Viewpoint (metres) Distance to Horizon (miles)