From a point 200m above the lake, the angle of elevation of a stationary helicopter is 30˚, and the angle of depression of reflection of the helicopter in the lake is 45˚. Find the height of the helicopter.

OR

If the angles of elevation of a tower from two points at distances a and b, where a > b from its foot and in the same straight line from it are 30˚ and 60˚ respectively, the find the value of .

A is the helicopter and D is its reflection in the lake.

Let the height of the helicopter be x. and BC = y.

In ΔABC,

y = √3(x – 100)m…..(1)

In ΔBCD,

y = (x + 100)m…….(2)

From equations 1 and 2,

x + 100 = √3(x – 100)

x + 100 = √3x - 100√3

√3x – x = 100 + 100√3

x(√3 – 1) = 100(1 + √3)

Rationalizing the fraction, we get

OR

Let the height of the tower, AD = h m

Now, in ΔADC, we have,

h = b√3m

…(1)

Similarly, in ΔADB, we have,

h√3 = a – b

Putting the value of b from equation 1, we get,

…..(2)

From (1) and (2)

Hence, the value of is 4.