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The height of a tower is h and the angle of elevation of the top of the tower from a point on the plane is α. On moving a distance h/2 towards the tower, the angle of elevation becomes β. The value of cot α - cot β is

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Important Questions on Some Applications of Trigonometry

EASY

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

∆ XYZ

, the measure of angle

Y

90 °

. If

\sec X = \frac{17}{8}

, and

XY = 0.8 cm

, what is the length (in

cm

) of side

XZ

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:

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

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?

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:

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 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

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point

A

, with uniform speed. At that point, angle of depression of the boat with the man's eye is

30 °

(Ignore man's height). After sailing for

20

seconds, towards the base of the tower (which is at the level of water), the boat has reached a point

B

, where the angle of depression is

45 ° .

Then the time taken (in seconds) by the boat from

B

to reach the base of the tower 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 :

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

P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are

60^{o}

and

30^{o}

, respectively and the distance between them is

84 \sqrt{3} m

. What is the height (in

m

) of the pole?

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 person standing on the top of a building of height

60 \sqrt{3}

feet observed the top of a tower to lie at an elevation of

45 ° .

That person descended to the bottom of the building and found that the top of the same tower is now at an angle of elevation of

60 ° .

The height of the tower (in feet) is

MEDIUM

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

In triangle

ABC

measure of angle

B

90 °

. If

\sec A = \frac{25}{7}

and

AB = 14 cm

, what is the length (in

cm

) of side

BC

MEDIUM

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

The angle of elevation of a jet plane from a point

A

on the ground is

60 ° .

After a flight of

20

seconds at the speed of

432 km / hour

, the angle of elevation changes to

30 ° .

If the jet plane is flying at a constant height, then its height is:

EASY

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

The value of the expression

cosec (85^{ο} + θ) - \sec (5^{ο} - θ) - \tan (55^{ο} + θ) + \cot (35^{ο} - θ)

is :

MEDIUM

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

Two vertical poles are

150 m

apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

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

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

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

The height of a tower is h and the angle of elevation of the top of the tower from a point on the plane is α. On moving a distance h/2 towards the tower, the angle of elevation becomes β. The value of cot α - cot β is

Important Questions on Some Applications of Trigonometry

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