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1. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30 with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60. What is the distance between the base of the tower and the point P ?
2. The angle of elevation of a ladder leaning against a wall is 60 and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
3. The angle of elevation of the sun, when the length of the shadow of a tree _/3 times the height of the tree, is:
Answer: Option A
Explanation:Let AB be the tree and AC be its shadow, So as per question, the shadow of a tree is √3 times the height of the tree.
Lets assume h be the height of the tree.
AB/AC = tanθ
=> h/√3h = tanθ
=> tanθ = 1/√3
So, Angle = 30∘
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4. From height of 8 mts a ball fell down and each time it bounces half the distnace back. What will be the distance travelled
Answer: Option A
Explanation:8+4+4+2+2+1+1+0.5+0.5+ and etc .. = 24
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5. The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.
Answer: Option B
Explanation:Area of the field = Total cost/Rate = (333.18/24.68) hectares =13.5 hectares.
= (13.5*10000) m^2 =135000m^2.
Let altitude = x meters and base = 3x meters.
Then, 1/2 *3x* x= 135000 or x^2 = 9000 or x= 300.
Therefore, base =900 m & altitude = 300m.
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6. Find the area of a rhombus one side of which measures 20 cm and one diagonal
Answer: Option A
Explanation:Lets assume other diagonal = 2x cm,
Since halves of diagonals and one side of rhombus form a right angled triangle with side as hypotenuse, we have:
(20)^2 =(12)^2+x^2 or x=?(20)^2-(12)^2 =?256=16 cm.
So, other diagonal = 32 cm.
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7. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 degree and 45 degree respectively. If the lighthouse is 100 m high, the distance between the two ships is:
8. On the two sides of a road are two tall buildings exactly opposite to each other. The height of the taller building is 60 m. If the angle of elevation from the top of the smaller building to the top of the taller one is 30° and the angle of depression from top of the taller building to the foot of the smaller one is 30°, then find the height of the smaller building.
Answer: Option C
Explanation:Let AB be the taller building of height 60m and CD be the smaller one of height h m.
tan30= DB/AB = DB/60 = 1/v3
DB = 34.64 m
tan30= AE/CE = AE/DB = 1/v3 = AE/34.64
AE = 60 - h = 20
h = 40 m
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9. Satish was looking at a new building Kohli Towers constructed having height of 200 m. The angle of elevation of the top of building from a point on ground is 30°. What is the distance of the point from the foot of the building?
Answer: Option C
Explanation:Given towers Angle APB = 30°. And AB = 200 m
AB/AP = tan 30° = 1/√3
AP = (AB x √3) m
200√3 m = 200 x 1.73 = 346m
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10. Jaya Towers and Karuna towers are two tall buildings standing 400 metres apart. Two fast flying birds were sitting on top of these two towers and were aiming at catching the grains put up in one place. Jaya Tower's height is 300 metres and the grains 160 metres apart from Jaya Towers. Both the birds were flying down at the same speed and reached the grains spot at the same time. What is the approximate height of Karuna Towers?
Answer: Option B
Explanation:Jaya Tower is 300 metre tall
Lets assume Karuna Tower's height be x
Distance of grains spot from Jaya Towers -- 160 metres.
Both the birds were flying down at the same speed and reached the grains spot at the same time
i.e Time taken for bird on Jaya tower to reach grain = Time taken for bird on Karuna tower to reach grain
Or Distance travelled by bird on Jaya tower / Speed of bird on Jaya tower = Distance travelled by bird on Karuna tower / Speed of bird on Karuna tower ->(1)
But as it is given that both the birds travelled with same speed, Speed of bird on Jaya tower = Speed of bird on Karuna tower. Applying this to equation (1) we get,
Distance travelled by bird on Jaya tower = Distance travelled by bird on Karuna tower -> (2)
Apply Pythagoras theorem, we know that (Distance travelled by bird on Jaya tower)2 = (300)2 + (160)2 -> (3)
Again by applying Pythagoras theorem to the other triangle. (Distance travelled by bird on Karuna tower)2 = (400-160)2 + x2 -> (4)
From equations 2,3 and 4 we get
(300)2 + (160)2 = (400-160)2 + x2
115600 = 57600 + x2
58000 = x2
240.83 m = x
Therefore x is approximately 240 m
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