Geometry & MeasuresStudy Notes

Worked Example 2: Finding an Angle

Part of Trigonometry (SOH CAH TOA)GCSE Mathematics

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 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 6

Practice

19 questions

Recall

7 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

Answer: 36.9°

Keep building this topic

Read this section alongside the surrounding pages in Trigonometry (SOH CAH TOA). That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Trigonometry (SOH CAH TOA)

Which trigonometric ratio connects the opposite side and the hypotenuse in a right-angled triangle?

  • A. tan θ = opposite / adjacent
  • B. cos θ = opposite / hypotenuse
  • C. sin θ = opposite / hypotenuse
  • D. sin θ = adjacent / hypotenuse
1 markfoundation

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.

2 marksstandard

Quick Recall Flashcards

SOH CAH TOA
Sin = O/H, Cos = A/H, Tan = O/A. Pick based on which two sides you have or need.
SOH CAH TOA
sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj

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