From the top of a hill 240 m high, the angles of depression of the top and bottom of a pole are 30º and 60º, respectively. The difference (in cm) between the heights of the pole and its distance from the hill is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 80(2-√3)
In ABC,
tan60 = AB/AC
√3 = 240/AC
AC = 80√3
In ADE,
tan30 = AE/DE
1/√3 = (240 - h)/80√3
240 - h = 80
h = 160m
Required difference = 160 - 80√3
= 80(2 - √3).