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**Q.1. If a pole 6 m high casts a shadow 2√3 m long on the ground, find the Sun’s elevation.Ans.**

⇒ θ = 60°

Ans.

h = 100√3 m

Ans.

In ΔOAP, we have

Also in ΔOAB,

...(ii)

From (i) and (ii), we get

or

**Q.4. If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β, prove that the height of the cloud is Ans.** Let AB be the surface of the lake and let P be a point of observation (Fig. 11.58) such that AP = h metres. Let C be the position of the cloud and C' be its reflection in the lake. Then, CB = C'B. Let PM be perpendicular from P on CB. Then, ∠CPM = α and ∠MPC‘ = β. Let CM = x.

Then, CB = CM + MB = CM + PA = x + h

In ΔCPM, we have

⇒ AB = x cot α

In ΔPMC’, we have

⇒ AB = (x + 2h) cotβ ...(ii)

From (i) and (ii), we have

Hence, the height CB of the cloud is given by

CB = x + h ⇒

⇒ **Q.5. The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60° and 30° respectively. Find the height of the balloon above the ground.Ans.** Let height of balloon = h m

In rt. ΔGDC,

...(i)

According to question

DC = EF

Height of the balloon above the ground is 8 m.

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