This study notes covers Worked Example 2: Finding an Angle within Trigonometry (SOH CAH TOA) for GCSE Mathematics. Revise Trigonometry (SOH CAH TOA) in Geometry & Measures for GCSE Mathematics with 19 exam-style questions and 7 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 2: Finding an Angle
A right-angled triangle has opposite side 6 cm and adjacent side 8 cm. Find the angle.
Step 1 Identify the ratio
We have: O = 6, A = 8
O and A → use Tan
Step 2 Write and substitute
tan θ = 68 = 0.75
Step 3 Use inverse tan (tan⁻¹)
θ = tan⁻¹(0.75)
θ = 36.9° (1 d.p.)
On your calculator: press SHIFT then tan, then 0.75
Practice questions for Trigonometry (SOH CAH TOA)
Which trigonometric ratio connects the opposite side and the hypotenuse in a right-angled triangle?
For the triangle shown, a student chooses to use sin to find the missing side. Explain why they chose sin rather than one of the other trigonometric ratios.