The angles of elevation of the top of a tree 220 meters high from two points lie on the same side of the tree are 30° and 45°. What is the distance (in metres) between the two points?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 161.05
Let the distance between two point = x meter
In △DAB
tan 45° = 220/AB
⇒ AB = 220 m
In △DAC
tan 30° = 220/AC
⇒ 1/√3 = 220/AC
⇒ AC = 220√3
Hence,
x = AC - AB = 220√3 - 220 = 220(√3 - 1) = 220 × 0.732 = 161.04 m