142. From a tower 125 metres high, theangles of depression of two ob-j

1.	142. From a tower 125 metres high, theangles of depression of two ob-jects, which are in horizontal linethrough the base of the tower, are45° and 30° and they are on thesame side of the tower. The dis-tance (in metres) between theobjects is(A) 125V3(B) 125(3-1)(C) 125/(3-1)(D) 125(V3 + 1)
Answer» AB = TOWERIn triangle ABC tan 45 = AB/BC1 = AB/AC = AB:BC = 1:1 In triangle ABD tan 30 = AB/BD= AB:BD = 1: root(3) CD = BD - BC = (root(3) - 1) units AB = 1 unit = 125 metres CD = (root(3) - 1) units = 125(root(3) - 1) metres (B) is correct option

142. From a tower 125 metres high, theangles of depression of two ob-jects, which are in horizontal linethrough the base of the tower, are45° and 30° and they are on thesame side of the tower. The dis-tance (in metres) between theobjects is(A) 125V3(B) 125(3-1)(C) 125/(3-1)(D) 125(V3 + 1)

Answer»

AB = TOWERIn triangle ABC tan 45 = AB/BC1 = AB/AC = AB:BC = 1:1

In triangle ABD tan 30 = AB/BD= AB:BD = 1: root(3)

CD = BD - BC = (root(3) - 1) units

AB = 1 unit = 125 metres

CD = (root(3) - 1) units = 125(root(3) - 1) metres

(B) is correct option