Question

[Take V3 = 1.732.]
29. The angles of elevation of the top of a tower from two points at distances
of 4 m and 9 m from the base of the tower and in the same straight line
with it are complementary. Show that the height of the tower is 6 metres.​

Answer 1

Answer:

The given situation can be represented as,

[ refer in 1st pic I attached]

Let height of the tower be h m.

Given, the angles of elevation of the top of tower from the two points are complementary.

∴ ∠ACB = θ and ∠ADB = 90 – θ

In ∆ABC, [ refer in 2nd pic I sent ]

In ∆ABD,[ refer in 2nd pic I sent]

∴ Height of the tower = h = 4 tan θ = 4 × = 6 m             (Using (1))

Thus, the height of the tower is 6 m.

I attached 2 important files also

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