Question

From the top of a tower 100 m high a man observes the angles of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line find the distance between the two ships A and B to the nearest metre.

(Use Mathematical Tabels for this question)

Answer 1

Let AC = x, BC = y

Now ∠A = 45°   ...(Alternative angles)

And ∠B = 38°   ...(Alternative angles)

In ΔACD,

`tan 45^circ = 100/x`

`\implies 1 = 100/x`

∴ x = 100   ...(1)

In ΔBCD,

 `tan 38^circ = 100/y`

`0.7812 = 100/y`

`y = 100/0.7812 ≈ 128`

Hence, Distance between two ships A, B

= x + y

= 100 + 128

= 228 m