From the top of a 195-m high cliff, the angles of desperssion of the top and bottom of a tower are 30° and 60°, respectively. Find the height of the tower (in cm).
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 130
Formula used:
tanθ = perpendicular/base ----- (1)
Calculations:
Let us take BD = x and AB = y, where BD = AE
CE = 195 - x
⇒ tan 30° = (195 - x)/y
⇒ y = (195 - x)√3 ---- (1)
Now, tan 60° = 195/y
⇒ y = 195/√3 ---- (2)
Equating equation (1) and (2)
⇒ (195 - x)√3 = 195/√3
⇒ 195 = 585 - 3x
⇒ 3x = 390
⇒ x = 130.
Hence, height of the tower is 130 m.