From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

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KollegeApply · Accepted Answer

Given that: height of cliff is 25 m and angle of elevation of the tower is equal to angle of depression of foot of the tower that is $\theta$. Now, the given situation can be represented as, Here, D is the top of cliff and BE is the tower. Let CE = h, AB=x. Then, AB=DC= = x Here, we have to find the height of the tower BE. So, we use trigonometric ratios. In a triangle ABD, $\Rightarrow$ tan $\theta$= AD/AB $\Rightarrow$ tan $\theta$=25/x (1) Again in a triangle,DCE tan $\theta$=(CE)/(CD) $\Rightarrow$ tan $\theta$=h/x $\Rightarrow$25/x=h/x [using 1] $\Rightarrow$h=25 Thus, height of the tower = BE = BC + CE = (25 + 25) m = 50 m [Solution diagram: 63514_solution_1.png]

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