Geometry and TrigonometryMediumLadder length from its foot distance and angle
Geometry and Trigonometry practice question
A ladder leans against a vertical wall, making a 60° angle with the level ground. The foot of the ladder is 2 metres from the wall. How long is the ladder, in metres?
Answer: 4
The 2-metre distance is the side adjacent to the 60° angle, and the ladder is the hypotenuse: cos 60° = 2/L, so L = 2 / (1/2) = 4.
Common wrong answers
- If you answered 1
- 1 multiplies 2 by cos 60° instead of dividing; the ladder is the hypotenuse, which is longer than 2.
- If you answered 3.46
- 3.46 is 2 tan 60°, the HEIGHT the ladder reaches on the wall.
- If you answered 2.31
- 2.31 is 2 ÷ sin 60°, using the wrong ratio for the adjacent side.
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