SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Trigonometry, SMB-024

Express `tan theta` as a fraction in its simplest form.  (3 marks)

Show Answers Only

`tan theta = (2sqrt5)/5`

Show Worked Solution

`text{Let unknown side =}\ x`

`text{By Pythagoras:}`

`6^2` `=x^2 + 4^2`  
`x^2` `=36-16`  
`x` `=sqrt20\ \ (x>0)`  

 

`:.tan theta` `=4/sqrt20`  
  `= 4/(2sqrt5) xx sqrt5/sqrt5`  
  `= (2sqrt5)/5`