Geometry and TrigonometryEasy–MediumLadder against a wall
Geometry and Trigonometry practice question
A ladder 10 feet long leans against a vertical wall, with its foot on level ground 6 feet from the base of the wall. How many feet up the wall does the ladder reach?
Answer: 8
The wall, the ground and the ladder form a right triangle with hypotenuse 10 and one leg 6. The other leg is √(10² − 6²) = √(100 − 36) = √64 = 8.
Common wrong answers
- If you answered 4
- 4 is 10 − 6. Lengths in a right triangle don't subtract directly; the squares do: 100 − 36 = 64.
- If you answered 16
- 16 is 10 + 6, but the height must be shorter than the ladder itself.
- If you answered 136
- 136 is 10² + 6², adding the squares — that finds a hypotenuse. Here 10 IS the hypotenuse, so subtract: 100 − 36.
More Geometry and Trigonometry questions
- Easy–Medium
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A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
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