Trigonometry to Find Angles (Edexcel IGCSE Maths)

SOHCAHTOA - Finding Angles

Spec point — 4.8B

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 t rigonometric 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

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

• STEP 4 Substitute the fraction into the inverse trigonometric function

  • You normally need to press SHIFT on your calculator first

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

• 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

Worked Example Find the value of the angle $y$° in the following triangle.

Give your answer to 1 decimal place.

Answer:

First label the triangle

We know A and H - that's CAH or $\mathrm{cos}θ=\frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}$

$\cos ( y ) = \frac{8}{23}$

Use inverse cos to find $y$

$y = \cos ^{- 1} ( \frac{8}{23} )$

Enter on your calculator

$y=69.6455...$

Round to 1 decimal place

$y=69.6^{\circ}$