# The horizontal di

In the figure, let CD be the first tower and AB, the second tower. We are given that the distance between the two towers is 60 m. Join C and B. We thus get CB = 60 m. Again, we are given that the angle of depression of the top of the first tower from the top of the second tower is 30°. We draw a horizontal line parallel to BC from A to F. Then we get FAD = 30°. Now, we draw a line from the top of the first tower onto the second tower parallel to BC to the point E. We get a right-angled triangle ADE with right angle at E. Then ADE = 30°.We are also given that the height of the second tower is 90 m. So, AB = 90m. We are told to find the height of the first tower, that is CD.

Note that, BC = ED = 60m.

To find CD, we use the trigonometric ratio tan on ∆ADE to find AE.

In ∆AED,

or,

Now we just see that we can get the height of the first tower by subtracting the value of AE from AB to get BE which is equal to CD.

Height of the first tower = DC = AB-AE = 90-60/√3 = 55.35m.

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