Question

A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60° with the horizontal and the height of the house be 6√3 m, then the length of the ladder is

(a) 12√3 m

(b) 12 m

(c) \(\frac{12}{\sqrt3}\)m

(d) None of these

Answer 1

(b) 12 m

Let AB be the height of the house. Given AB = 6√3m

Let AC be the ladder whose length AC = x metres (say) 

Given ∠ACB = 60° 

∴ In rt. ΔABC, \(\frac{AB}{AC}\) = sin 60°

⇒ \(\frac{6\sqrt3}{x}\) = \(\frac{\sqrt3}{2}\) ⇒ \(x\) = 12 m.