Trigonometry to Find Angles (Edexcel GCSE Maths: Foundation): Revision Note

SOHCAHTOA - Finding angles

How can I use SOHCAHTOA to find missing angles?

• STEP 1
  Label the sides of the triangle as H, O and A

  • H is the longest side opposite the right angle

  • O is opposite the given angle

  • A is next to the given angle

• STEP 2
  Identify which trigonometric ratio to use: sin, cos or tan

  • Write down the letters of the lengths you are given

  • Find the two letters in SOHCAHTOA to identify which ratio to use

    • If you have O and A then use tan

• STEP 3
  Substitute the values into the relevant trigonometric formula

  • The angle will be unknown

    • $\tan \left(\theta \right)=\frac{3}{4}$ 

• STEP 4
  Substitute the fraction into the inverse trigonometric function

  • You normally need to press SHIFT on your calculator first

    • $\tan \left(\theta \right)=\frac{3}{4}$ leads to $\theta ={\tan }^{-1}\left(\frac{3}{4}\right)$

• STEP 5
  Type the expression into your calculator

  • The question might ask you to round your answer

  • If not then round to one decimal place