When viewed from the top of a tower of height 100 metres, the angle of elevation of a boat is 30 degrees. The boat moved "x" metres towards the tower and the angle of elevation changed to 5 degrees. Find the value of "x"?

Correct option is C

Given:
Height of the tower (h) = 100 m
Initial angle of elevation = 30°
Final angle of elevation = 45°
Boat moves x metres closer to the tower

Use tan θ = height / distance
Solution:​
Let initial horizontal distance from the boat to the base of the tower be D
Then:
tan(30°) = 100 / D
tan(45°) = 100 / (D − x)

We will solve both equations to find x
From first triangle:
tan(30°) = 1/√3 => D = 100√3

From second triangle:
tan(45°) = 1 => D − x = 100
=> x = D − 100 = 100√3 − 100

Take 100 common:
=> x = 100(√3 − 1)

Final Answer:
(C) $$100(\sqrt{3} - 1)$$​​