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IMPORTANT

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In $Δ A B C,$ base $B C$ and area of triangle $' Δ'$ are fixed. Locus of the centroid of $Δ A B C$ is a straight line that is

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Important Questions on Properties of Triangles, Heights and Distances

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 80

Δ A B C, ∠ A = \frac{π}{2}, A A_{1}

and

A A_{2}

are the median and altitude, respectively. If

∠ B A A_{1} = ∠ A_{1} A A_{2} = ∠ A_{2} A C,

then

\sin^{3} \frac{A}{3} \cdot \cos \frac{A}{3}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 81

At a point

A

, the angle of elevation of a tower is such that its tangent is

\frac{5}{12},

on walking

120 m

nearer the tower the tangent of the angle of elevation is

\frac{3}{4} .

The height of the tower is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 82

An observer on the top of a cliff

200 m

above the sea level, observes the angles of depression of two ships on opposite sides of the cliff to be

45 °

and

30 °

, respectively. The distance between the ships if the line joining them points to the base of cliff, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 83

A tower is observed from two stations

A

and

B

, where

B

is East of

A

at a distance of

200 m

. The tower is due North of

A

and due West of

B .

The angles of elevation of the tower from

A

and

B

are complementary. The height of the tower is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 84

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of

100 m

from its base is

45 ° .

If the angle of elevation of the top of the complete pillar at the same point is to be

60 °,

then the height of the incomplete pillar is to be increased by

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 85

A tree is broken by wind, its upper part touches the ground at a point

10 m

from the foot of the tree and makes an angle of

45 °

with the ground. The entire length of the tree is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 86

If a flagstaff

6 m

high placed on the top of a tower throws a shadow of

2 \sqrt{3} m

along the ground, then the angle (in degree) that the Sun makes with the ground, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 87

The angle of elevation of the top of a tower from the top and bottom of a building of height

a

are

30 °

and

45 °,

respectively. If the tower and the building stand at the same level, the height of the tower is

In ΔABC, base BC and area of triangle 'Δ' are fixed. Locus of the centroid of ΔABC is a straight line that is

Important Questions on Properties of Triangles, Heights and Distances

Learn and Prepare for any exam you want !

In $Δ A B C,$ base $B C$ and area of triangle $' Δ'$ are fixed. Locus of the centroid of $Δ A B C$ is a straight line that is