Question

The angle of elevation of the top of an incomplete tower at a point 40 m from its base is 45°. If the elevation of the completed tower at the same point is 60°, then the height through which the tower has been raised is
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Answer 1

Step-by-step explanation:

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Answer 2

Let PA be the unfinished tower.

Let B be the point of observation i.e. 120 m away from the base of the tower.

Now, AB = 120m

Let, ∠ABP=45°

Let h m be the height by which the unfinished tower be raised such that its angle of elevation of the top from the same point becomes 60°.

Let CA = h &∠ABC=60°

In triangle ABP,

tan45°=ABPA

⇒1=120PA

⇒PA=120M

Now, in triangle ABC,

tan60°=ABCA

3=120120+h

h+120=1203

h=120(3−1)

h=120(1.732−1)→(as3=1.732)

h=120×0.732

h=87.84m