EASY

JEE Main

IMPORTANT

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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 $C$ to $P$ 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

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Important Questions on Heights and Distances

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 29 June 2022 Shift 2>Q 24

From the base of a pole of height

20

meter, the angle of elevation of the top of a tower is

60 °

. The pole subtends an angle

30 °

at the top of the tower. Then the height of the tower is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 25 July 2022 Shift 1>Q 25

A tower

P Q

stands on a horizontal ground with base

Q

on the ground. The point

R

divides the tower in two parts such that

Q R = 15 m

. If from a point

A

on the ground the angle of elevation of

R

60 °

and the part

P R

of the tower subtends an angle of

15 °

A

, then the height of the tower is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 27 July 2022 Shift 1>Q 26

Let a vertical tower

A B

of height

2 h

stands on a horizontal ground. Let from a point

P

on the ground a man can see upto height

h

of the tower with an angle of elevation

2 α

. When from

P

, he moves a distance

d

in the direction of

\vec{A P}

, he can see the top

B

of the tower with an angle of elevation

α

. If

d = \sqrt{7} h

, then

\tan α

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 27 July 2022 Shift 2>Q 27

The angle of elevation of the top

P

of a vertical tower

P Q

of height

10

from a point

A

on the horizontal ground is

45 °

. Let

R

be a point on

A Q

and from a point

B

, vertically above

R

, the angle of elevation of

P

60 °

. If

∠ B A Q = 30 °, A B = d

and the area of the trapezium

P Q R B

α

, then the ordered pair

(d, α)

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 28 July 2022 Shift 2>Q 28

A horizontal park is in the shape of a triangle

O A B

with

A B = 16

. A vertical lamp post

O P

is erected at the point

O

such that

∠ P A O = ∠ P B O = 15 °

and

∠ P C O = 45 °

, where

C

is the midpoint of

A B

. Then

{(O P)}^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Heights and Distances>JEE Main - 29 July 2022 Shift 1>Q 29

The angle of elevation of the top of a tower from a point

A

due north of it is

α

and from a point

B

at a distance of

9

units due west of

A

\cos^{- 1} (\frac{3}{\sqrt{13}})

. If the distance of the point

B

from the tower is

15

units, then

\cot α

is equal to

Let AB and PQ be two vertical poles, 160m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let π8 and θ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan2θ is equal to

Important Questions on Heights and Distances

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