In right ΔBAD,
tan 45° = \(\frac{AB}{AD}\)
⇒ \(\frac{AB}{AD}\) = 1 (\(\because\) tan 45° = 1)
⇒ AD = AB = 30 m (\(\because\) AB = Height of house = 30 m)
In right Δ CAD,
tan 60° = \(\frac{AC}{AD}\)
⇒ AC = AD\(\sqrt3\) (tan 60° = \(\sqrt3\))
= 30\(\sqrt3\).
⇒ AB + BC = 30\(\sqrt3\)
⇒ BC = 30\(\sqrt3\) - AB = (30\(\sqrt3\) - 30)m
⇒ BC = 30(\(\sqrt3\) - 1)m