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°
Q.2. If the angle of elevation of a tower from a distance of 100 m from its foot is 60°, then what will be the height of the tower?
Ans: Let h be the height of the tower.
h = 100√3 m
Q.3. A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, find the height of the centre of the balloon.
Ans: In Fig. 11.55, O is the centre of the balloon, whose radius OP = r and ∠PAQ = θ. Also, ∠OAB = φ. Let the height of the centre of the balloon be h. Thus OB = h.
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 a 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 the 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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