Pythagoras' Theorem — O/L Mathematics

How do I practise Pythagoras' Theorem?

1 question with a worked solution

1. A 13-metre ladder rests against a vertical wall such that its foot is 5 metres away from the base of the wall. How high up the wall does the top of the ladder reach?
   1. A) 12.5 m
   2. B) 10 m
   3. C) 12 m
   4. D) 11 m
   Check my answer

   Correct answer: C) 12 m

   Form a right triangle: hypotenuse c = 13 m, base b = 5 m. By Pythagoras' theorem: a² + b² = c² → h² + 5² = 13² → h² + 25 = 169 → h² = 144 → h = 12 m.

   Show worked solution

   Step 1: Model scenario as right-angled triangle with ladder as hypotenuse (c = 13) and distance from wall as base (b = 5). Step 2: Pythagoras' theorem: h = √(13² - 5²). Step 3: Evaluate: √(169 - 25) = √144 = 12 m. Answer: 12 m.
   Modelled on: the O/L Mathematics examination pattern

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Where does Pythagoras' Theorem fit in the syllabus?

Grade 11 · Term 2