Question

From the top of a light house 100 m high, the angles of depression of two ships are observed as ${48}^{\circ }and{36}^{\circ }$ respectively. Find the distance between the two ships (in the nearest metre) If :

(i) the ships are on the same side of the light house,

(ii) the ships are on the opposite sides of the light house.

Answer 1

Science

AB = 100 m (given

$\tan {48}^0=\frac{AB}{BC}\to BC=\frac{AB}{\tan {48}^0}=100\cot {48}^0=90.04\tan {36}^0=\frac{AB}{DB}\to DB=\frac{AB}{\tan {36}^0}=100\cot {36}^0=137.64$

(i) when both are in same direction, Distance between them =DB-CB=137.64-90.04 =47.6

(ii)when both are in opposite direction , Distance between them=DB+CB=137.64+90.04=227.68