Answer :

In the above figure, let AB be the tower and P and D be the positions of the two cars at an instant, observed from A. join A and E. The angles of depression are ∠DAE and ∠PAE. Given that, PD = 100 m. Since AE is parallel to BD, so, ∠ADB = ∠DAE = 45° and ∠APB = ∠PAE = 60°. Join P,D and A,B. We get two right-angled triangles ∆ABD and ∆ABP. We are to find AB. We use trigonometric ratio tan for both the triangles, using AB as height and BP as base for ∆ABP and AB as height and BD as base for ∆ABD.

From ∆ABD,

or, AB = BD

From ∆APB,

or, BD = BP√3

or, BP + 100 = BP√3

or, BP(√3-1) = 100

or,

Hence, the height of the tower is, AB = BD = BP + 100 = 136.61 + 100 = 236.61m

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