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° = `100/x`

`\implies` 1 = `100/x`

∴ x = 100   ...(1)

In ΔBCD,

 tan 38° = `100/y`

0.7812 = `100/y`

y = `100/0.7812 ≈ 128`

Hence Distance between two ships A, B

= x + y

= 100 + 128

= 228 m