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A tower and a pole stand vertically on the same level ground. It is observed that the angles of depression of top and foot of the pole from the top of the tower of height $60 m$ is $30 °$ and $60 °$ respectively. Find the height of the pole in metre.

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Important Questions on Some Applications of Trigonometry

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

If the angles of elevation of the top of a tower from three collinear points

A, B

and

C

on a line leading to the foot of the tower are

30 °, 45 °

and

60 °

respectively, then the ratio

A B : B C

, is

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes

18 \min

for the angle of depression of the car to change from

30 °

45 °

, then the time taken (in

\min

) by the car to reach the foot of the tower is

HARD

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point

A

on the path, he observes that the angle of elevation of the top of the pillar is

30^{°}

. After walking for

10

minutes from

A

in the same direction, at a point

B

, he observes that the angle of elevation of the top of the pillar is

60^{°}

. Then the time taken (in minutes) by him, from

B

to reach the pillar, is

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A B C

is a triangular park with

A B = A C = 100

metres. A vertical tower is situated at the mid-point of

B C

. If the angles of elevation of the top of the tower at,

A

and

B

are

{c o t}^{- 1} (3 \sqrt{2})

and

{c o s e c}^{- 1} (2 \sqrt{2})

respectively, then the height of the tower (in metres) is

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A bird is sitting on the top of a vertical pole

20 m

high and its elevation from a point

O

on the ground is

45 °

. It flies off horizontally straight away from the point

O

. After one second, the elevation of the bird from

O

is reduced to

30 °

. Then the speed (in

m / s

) of the bird is

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

Two poles standing on a horizontal ground are of heights

5 m

and

10 m

respectively. The line joining their tops makes an angle of

15 °

with the ground. Then the distance

(

m)

between the poles, is

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

P Q R

is a triangular park with

P Q = P R = 200 m

. A T.V. tower stands at the mid-point of

Q R

. If the angles of elevation of the top of the tower at

P, Q

and

R

are respectively,

45 °, 30 °

and

30 °

, then the height of the tower (in

m

) is:

HARD

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A peacock perched on the top of a

12 m

high tree spots a snake moving towards its hole at the base of a tree from a distance equal to thrice the height of the tree. The peacock flies towards the snake in a straight line, and they both move at the same speed. At what distance from the base of the tree will peacock catch the snake?

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A straight highway leads to the foot of a

50 m

tall tower. From the top of the tower the angle of depression of the two cars on the highway are

30 °

and

60 °

. Then the distance between the two cars is

HARD

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A sphere with centre $O$ sits atop a pole as shown in the figure. An observer on the ground is at a distance $50 m$ from the foot of the pole. She notes that the angles of elevation from the observer to points $P$ and $Q$ on the sphere are $30 °$ and $60 °$ , respectively. Then, the radius of the sphere in meters is

Question Image

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

The angle of the top of a vertical tower standing on a horizontal plane is observed to be

45 °

from a point A on the plane. Let

B

be the point

30 m

vertically above the point A. If the angle of elevation of the top of the tower from

B

30 °

, then the distance (in m) of the foot of the tower from the point

A

is:

HARD

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

If the angle of elevation of a cloud from a point

P

which is

25 m

above a lake be

30 °

and the angle of depression of reflection of the could in the lake from

P

60 °

, then the height of the cloud (in meters) from the surface of the lake is :

EASY

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

A ladder $10 m$ long is leaning against a vertical wall. It makes an angle of $60 °$ with the ground. How far is the foot of the ladder from the wall?

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

Two vertical poles of height,

20 m

and

80 m

stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is:

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

X is $5 m$ tall and he notices that he casts a shadow that is $3 m$ long. He then measures that the shadow cast by his school building is $30 m$ long. How tall is the building?

HARD

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

The angle of elevation of a cloud

C

from a point

P, 200 m

above a still lake is

30^{o}

. If the angle of depression of the image of

C

in the lake from the point

P

60^{o}

, then

P C

(in

m

) is equal to

HARD

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

The angle of elevation of the summit of a mountain from a point on the ground is

45 °

. After climbing up one km towards the summit at an inclination of

30 °

from the ground, the angle of elevation of the summit is found to be

60 °

. Then the height (in km) of the summit from the ground is :

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

Let a vertical tower

A B

have its end

A

on the level ground. Let

C

be the mid-point of

A B

and

P

be a point on the ground such that

A P = 2 A B

. If

∠ B P C = β

, then

\tan β

is equal to:

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

Let

10

vertical poles standing at equal distances on a straight line, subtend the same angle of elevation

α

at a point

O

on this line and all the poles are on the same side of

O

. If the height of the longest pole is

h

and the distance of the foot of the smallest pole from

O

a

; then the distance between two consecutive poles, is

MEDIUM

Mathematics>Trigonometry>Some Applications of Trigonometry>Heights and Distances

Consider a triangular plot

A B C

with sides

A B = 7 m,

B C = 5 m

and

C A = 6 m .

A vertical lamp-post at the mid-point

D

A C

subtends an angle

30 °

B .

The height (in

m

) of the lamp-post is:

A tower and a pole stand vertically on the same level ground. It is observed that the angles of depression of top and foot of the pole from the top of the tower of height 60 m is 30° and 60° respectively. Find the height of the pole in metre.

Important Questions on Some Applications of Trigonometry

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A tower and a pole stand vertically on the same level ground. It is observed that the angles of depression of top and foot of the pole from the top of the tower of height $60 m$ is $30 °$ and $60 °$ respectively. Find the height of the pole in metre.