From the top of a house A in a street, the angle of elevation and depression to the top and foot of another house B on the opposite side of the street are 45° and 30° respectively. If the height of house A is 18√3 m, then what is the height of house B?
Answer & explanation
Correct answer: option 4
AB = house A
PQ = house B
= PR + RQ
RQ = AB = 18 \(\sqrt {3}\)
tan \(\angle\)AQB = AB : BQ
1 : \(\sqrt {3}\)
↓ ↓
18 \(\sqrt {3}\) 18 \(\sqrt {3}\) × \(\sqrt {3}\) = 18 × 3 = 54 m
tan \(\angle\) PAR = PR : AR (AR = BQ)
1 : 1
↓ ↓
54 54 (BQ)
Therefore, height of house B = PQ = PR + RQ
= 54 + 18 \(\sqrt {3}\) = 18 (3 + \(\sqrt {3}\)) m