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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?

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Important Questions on Trigonometry

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

\frac{\sec θ - \tan θ}{\sec θ + \tan θ}

= \frac{3}{5}

, then the value of

\frac{cosec θ + \cot θ}{cosec θ - \cot θ}

is:

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

5 \sin^{2} θ + 14 \cos θ = 13, 0^{o} < θ < 90^{o}

, then what is the value of

\frac{\sec θ + \cot θ}{cosec θ + \tan θ}

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

The value of the expression

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

is :

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

Seema flies a kite on a

16 m

string at an inclination of

60 °

. What is the height of the kite above the ground?

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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?

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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}

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

\sec θ - \tan θ = \frac{x}{y}

(0 < x < y)

and

0^{ο} < θ < 90^{ο}

, then

\sin θ

is equal to :

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

If the height of a pole and the distance between the pole and a man standing nearby are equal, what would be the angle of elevation to the top of the pole?

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

Let A and B be two towers with the same base. From the mid-point of the line joining their feet, the angles of elevation of the tops of A and B are

30 °

and

45 °

, respectively. The ratio of the heights of A and B is _____.

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

A ladder is resting against a wall. The angle between the foot of the ladder and the wall is

45 °

and the foot of the ladder is

6.6 m

away from the wall. The length of the ladder (in

m

) is _____.

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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

, then

\tan θ + \cos θ + \sec θ =

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

The length of the shadow of a vertical pole on the ground is

36 m

. If the angle of elevation of the sun at that time is

θ

, such that

\sec θ = \frac{13}{12}

, then what is the height (in

m

) of the pole?

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

P

and

Q

are the 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^{°}

and

30^{°}

respectively and the distance between them is

84 \sqrt{3} m

. What is the height (in

m

) of the pole?

MEDIUM

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

A girl

1.2 m

tall can just see the sun over a

3.62 m

tall which is

2.42 m

away from her. The angle of elevation of the sun is:

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

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

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

Two poles of the height $12 m$ and $17 m$ stand vertically upright on a plain ground. If the distance between their feet is $12 m$ , find the distance between their tops.

EASY

Quantitative Aptitude>Geometry>Trigonometry>Trigonometric Equations, Functions, Identities and Ratios

∆ 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

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?

Important Questions on Trigonometry

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