In the figure, let AC be the tower of height 100m. The angles of depression are ∠BAE and ∠DAF. Given, AC = 100m. Since the line EF is parallel to the line BD, we have ∠BAE = ∠BAC = 30°, ∠DAF = ∠DAC = 45°, where B, D are the positions of the cars. Join B, C, and C, D. We get two right-angled triangles ∆ABC and ∆ADC, both right angled at C. We use trigonometric ratio tan for both the triangles, where BC is the base and Ac is the height (for ∆ABC) and CD is the base and AC is the height in ∆ACD. We are to find the distance between the two cars, i.e. BD.
DC = 100
Therefore, the distance between the two cars is
BD = BC + CD = 100√3 + 100 = 100(√3 + 1) = 273 m.
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