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A ladder leans against a vertical wall at an angle 60° to the wall, if...

Mathematics
WAEC 1992

A ladder leans against a vertical wall at an angle
60° to the wall, if the foot of the ladder is 5 metres
away from the wall, calculate the length of the
ladder.

  • A. \(\frac{5\sqrt3}{3}\)m
  • B. 5m
  • C. \(\frac{10\sqrt3}{3}\)m
  • D. 5√3m
  • E. 10m
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Correct Answer: Option C
Explanation

The ladder makes 60° inclination with the wall and its foot is 5m away from the wall.

Sketching the diagram, you will see that we have

\(sin 60 = \frac{5}{x}\) (where x is the length of the ladder)

⇒ \(x = \frac{5}{sin60}\)

\(x = \frac{10\sqrt{3}}{3}m\) 


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