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.
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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
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