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Mathematics Assignment Class 10 Chapter
9 Application of Trigonometry |
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Question 1 From the window 15 m high above the ground in a street,
the angles of elevation and depression of the top and foot of another house
on the opposite side of the street are 30o and 45o respectively.
Find the height of the opposite house.
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Take √3 = 1.732) [Answer 23.36] |
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Question 2 The
angle of elevation of an aeroplane from a point on the ground is 60o.
After a flight of 30 seconds, the angle of elevation changes to 30o.
If the plane is flying at a constant height of 3600√3 m, then find the
speed of the plane in km/hour. [Answer 864] km/h |
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Question 3 The angle of elevation of an aeroplane from a point on the
ground is 45o. After flying for 15 seconds, the angle of elevation
changes to 30o. If the aeroplane is flying at a constant height of
2500 m, then find the average speed of the aeroplane.
[Answer 439.2 km/h] |
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Question 4 A man standing on the deck of a ship, which is 10 m above
the water level, observes the angle of elevation of the top of a hill as 60o and
the angle of depression of the base of the hill as 30o. Find the
distance of the hill from the ship and the height of the hill. [Answer 10√3 m, 40 m] |
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Question 5 Two ships are approaching a light house from opposite
direction, the angle of depression of the two ships from the top of light
house are 30o and 45o. If the distance between the
two ships is 100 m, find the height of the light house. ( Take √3 = 1.732) [Answer 36.60 m] |
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Question 6 The angle of elevation of the cloud from a point 200 m
above the lake is 30o and the angle of depression of its
reflection in the lake is 60o. Find the height of the cloud from
the level of the lake . [Answer 400m] |
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Question 7: From the top of the tower, the angles of depression of two objects on the same side of the tower are found to be 𝞪 and 𝛃 (𝞪 > 𝛃). If the distance between the objects is K meters apart, then show that the height h of the tower is given by |
Question 8 From the top of the tower 60 m high, the angles of
depression of the top and bottom of a pole are observed to be 45o and
60o respectively. Find the height of the pole. [Answer 20(3 - √3)m ] |
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Question 9 A man in a boat, rowing away from a light house 100 m
high, takes 2 minutes to change the angle of elevation of the top of the
light house from 60o to 45o. Find the speed of the
boat. [Answer 50(3-√3)/3 m/min] |
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Question 10 The
angle of elevation of a cloud from a point 60m above a lake is 30o and
the angle of depression of the reflection of cloud in the lake is 60o.
Find the height of the cloud. |
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Question 11 Two equal poles on either side of the road 180m wide. The
angles of elevation of the top of the pillars are 60o and 30o at
a point between the pillars on the roadway. Find the height of the pillars
and the position of the point
[Ans: 77.94m, 135m] |
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Question 12 An aeroplane when flying at a height of 5000m above the
ground passes vertically above another plane at an instant when the angle of
elevation of the two planes from the same point on the ground are 60o and
45o respectively. Find the vertical distance between the two
planes at that instant.
Take √3 =
1.73 [Ans. 2116.7 ] |
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Question 13 From the top of a light house, the angles of depression of
two ships on the opposite sides of it are observed to be 30o and
60o. If the height of the light house be 150m, then find the
distances between two ships.
[Ans 200√3] |
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Question 14 An aeroplane flying horizontally 1000m above the ground is
observed at an angle of elevation 60o from the point on the
ground. After a flight of 10 seconds, the angle of elevation at the point of
observation changes to 30o. Find the speed of the plane in
m/s. Take √3 = 1.73
[Ans : 115.33 m/s.] |
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Question 15 A man on the top of the vertical tower observes a car
moving at a uniform speed coming directly towards it. If it takes 12 minutes
for the angle of depression to change from 30o to 45o,
how soon after this will the car reach the observation tower
? Take √3 =
1.73 [Ans 16.38 minutes] |
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Question 16 As observed from the top of a light house, 100m high above
the see level, the angles of depression of a ship, sailing directly towards
it ,changes from 30o to 60o. Find the distance
travelled by the ship during the period of observation. [Ans: 115.3 m] |
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Question 17 The angles of elevation of the tower from the two points
on the ground at distances a and b from the foot of the tower are
complementary. Prove that the height of the tower is √ab |
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