An 80√3 m long electric pole is standing in a park. Another pole is to be placed in the park, such that the top of first pole makes an angle of 30° with the top of second pole and an angle of 45° with the foot of second pole. What is the height of second pole? [Use √3 = 1.732]

An 80√3 m long electric pole is standing in a park. Another pole is to be placed in the park, such that the top of first pole makes an angle of 30° with the top of second pole and an angle of 45° with the foot of second pole. What is the height of second pole? [Use √3 = 1.732] Correct Answer 58.56 m

Let the height of the second pole be ‘x’ m and the distance between the poles be ‘d’ m as shown below

⇒ d = 80√3 m

Also,

⇒ tan 30° = (80√3 - x)/d

⇒ 1/√3 = (80√3 - x)/80√3

⇒ 80 = 80√3 - x

⇒ x = 80√3 - 80

⇒ x = 80(√3 - 1) = 80(1.732 - 1) = 80 × 0.732 = 58.56