EASY

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The angle of elevation and depression are usually measured by a device called

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Important Questions on Some Applications of Trigonometry

EASY

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

When a pole

6 m

high casts a shadow

2 \sqrt{3} m

long on the ground, then the angle of elevation of the sun is

EASY

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

The angle of elevation of the top of a tower from a point on the ground , which is $15 m$ away from the foot of the tower, is $60 °$ . The height of the tower is

EASY

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

As observed from the top of the light house, the angles of depression of two ships

P

and

Q

, anchored in the sea to the same side of the light house, are found to have measures

35 °

and

50 °

respectively. Then from the light house _____

EASY

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

If ratio of length of a vertical rod and length of its shadow is

\sqrt{3} : 1

, then the angle of elevation of sun will be

EASY

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

2 \sin θ +15 \cos^{2} θ = 7, 0^{ο} < θ < 90^{ο}

, then

\tan θ + \cos θ + \sec θ =

EASY

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

From the top of a

60 m

high tower, the angles of depression of the top and bottom of pillar are

30 °

and

60 °

respectively. Then the height of the pillar is

EASY

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

As observed from the top of the lighthouse, the angle of depression of the two ships A and B have measures

25

and

40

respectively. Then from the lighthouse _____.

EASY

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

Let

A B

and

P Q

be two vertical poles,

160 m

apart from each other. Let

C

be the middle point of

B

and

Q

, which are feet of these two poles. Let

\frac{π}{8}

and

θ

be the angles of elevation from

C

P

and

A

, respectively. If the height of pole

P Q

is twice the height of pole

A B

, then

\tan^{2} θ

is equal to

EASY

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

11 \sin^{2} θ - \cos^{2} θ + 4 \sin θ - 4 = 0, 0^{o} < θ < 90^{o}

, then what is the value of

\frac{\cos 2 θ + \cot 2 θ}{\sec 2 θ - \tan 2 θ}

EASY

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

A vertical pole fixed to the horizontal ground is divided in the ratio

3 : 7

by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground

18 m

away from the base of the pole, then the height of the pole (in meters) is :

EASY

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

A circus artist is climbing on a $20 m e t e r$ long rope which is tightly stretched and tied to the top of a vertical pole. If the angle made by the rope with the ground level is $30 °$ , then the height of the pole will be _____.

EASY

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

The value of

\frac{\tan 30^{o} cosec 60^{o} + \tan 60^{o} \sec 30^{o}}{\sin^{2} 30^{o} + 4 \cot^{2} 45^{o} - \sec^{2} 60^{o}}

is:

EASY

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

If the shadow of

10

m high tree is

10 \sqrt{3}

m, then the angle of elevation of sun is

EASY

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

A boy observed

20 m

away from the base of a

20 m

high pole, the angle of elevation of the top is _____

EASY

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

A tree breaks into two parts due to heavy wind such that the upper part makes an angle of

30 °

with plane. The place where the upper part of the tree touches the ground is at a distance of

10 m

from the base point of the tree. The height of the tree 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:

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

EASY

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

The angle of elevation of the top of a tower from a point on the ground, which is

30 m

away from the foot of the tower, is

45 °

. The height of the tower 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 :

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

The angle of elevation and depression are usually measured by a device called

Important Questions on Some Applications of Trigonometry

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