Question

as observed from the top of a 80 m tall light house ,the angles of depression of two ships on the same side of the light house in horizontal line with its base area 30° and 40° respectively. Find the distance between the two ships .Give your answer correct to the nearest metre.

Answer 1

Let AB be the height of the lighthouse and two ships be at distance of C and D.

In triangle ABC,

AB/BC = tan 40degree

80/BC = - 1.11721493092 = 1

BC = 80 m

In triangle ABD,

AB/BD = tan 30degree

80/ (BC+CD) = 1/root 3

80/ (80+CD) = 1/root 3

80 * root 3 = 80 + CD

80 (root 3 – 1) m = CD