MEDIUM

JEE Main

IMPORTANT

Earn 100

$P Q$ is a tower standing on a horizontal plane. $Q$ being its foot, $A$ and $B$ are the two points on the plane such that the $∠ Q A B = 90 °$ and $A B$ is $4 m$ . It is found that $\cot (P A Q) = \frac{3}{10}$ and $\cot (P B Q) = \frac{1}{2}$ . Find the height of the tower.

Important Questions on Heights and Distances

MEDIUM

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 9

A column is East South East of an observer, and at noon the end of the shadow is North-East of him. The shadow is

80 m

long and the elevation of the column at the observer’s station is

45 °

. Find the height of the column.

HARD

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 10

A tower is observed from two stations

A

and

B

. It is found to be due north of

A

and north-west of

B

B

is due east of

A

and distant from it

10

meters. The elevation of the tower as seen from

A

is the complement of the elevation as seen from

B

. Find the height of the tower.

MEDIUM

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 11

The elevation of a steeple at a place due south of it is

45 °

and at another place due west of the former place, the elevation is

15 °

. If the distance between the two places be

‘ a ’

, prove that the height of the steeple is

\frac{a (\sqrt{3} - 1)}{2 \sqrt[4]{3}} .

HARD

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 12

A person stands in the diagonal produced of the square base of a church tower, at a distance

2 a

from it, and observes the angles of elevation of each of the two outer corners of the top of the tower to be

30 °

, whilst that of the nearest corner is

45 °

. Prove that the breadth of the tower is

a (\sqrt{10} - \sqrt{2})

HARD

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 13

A person standing at a point

A

due south of a tower built on a horizontal plane observes the altitude of the tower to be

60 °

. He then walks to

B

due west of

A

and observes the altitude to be

45 °

and again at

C

A B

produced he observes it to be

30 °

. Prove that

B

is midway between

A & C

HARD

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 14

At each end of a horizontal base length of

2 a

, it is found that the angular height of a certain peak is

θ

and that at the middle point it is

ϕ

. Prove that the vertical height of the peak is

\frac{α \sin θ \sin ϕ}{\sqrt{\sin (ϕ + θ) \sin (ϕ - θ)}}

HARD

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 15

A

and

B

are two stations

1000 m .

Apart

P

and

Q

are two station in the same plane as

A B

and on the same side of it the angles

P A B, P B A,

Q A B

and

Q B A

are

75^{o}, 30^{o}, 45^{o}

and

90^{o}

respectively, find how far

P

is form

Q

and how far each is form

A

and

B

HARD

JEE Main

IMPORTANT

Plane Trigonometry Part 1>Chapter 13 - Heights and Distances>Examples XXXIII>Q 16

At a point on a horizontal plane the elevation of the summit of a mountain is found to be

22 ° 15^{'}

and at another point on the plane

1 km

farther away in a direct line its elevation is

10 ° 12'

, find the height of the mountain.

PQ is a tower standing on a horizontal plane. Q being its foot, A and B are the two points on the plane such that the ∠QAB=90° and AB is 4 m. It is found that cotPAQ=310and cotPBQ=12. Find the height of the tower.

Important Questions on Heights and Distances

Learn and Prepare for any exam you want !

$P Q$ is a tower standing on a horizontal plane. $Q$ being its foot, $A$ and $B$ are the two points on the plane such that the $∠ Q A B = 90 °$ and $A B$ is $4 m$ . It is found that $\cot (P A Q) = \frac{3}{10}$ and $\cot (P B Q) = \frac{1}{2}$ . Find the height of the tower.