Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 8

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The acute angle of a rhombus whose side is the geometric mean of its diagonals, is

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Important Questions on Solutions and Properties of Triangle

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 9

Let sides

a, b

and

c

of

∆ A B C

be related by the relation

a : b : c = 3 : 5 : 4

. Altitudes

A D, B E

and

C F

are dropped on

B C, C A

and

A B,

respectively. Let midpoints of

B C, C A

and

A B

be

P_{1}, P_{2}

and

P_{3}

,

respectively. If

P_{1} D + P_{2} E + P_{3} F = 42,

then the value of

a + b + c

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 10

Triangle

A B C

is right angled at

A .

The points

P

and

Q

are on hypotenuse

B C

such that

B P = P Q = Q C .

If

A P = 3

and

A Q = 4,

then the length

B C

is equal to

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 11

A B C

is a right-angled triangle of which

A

is the right angle,

B D

is drawn perpendicular to

B C

and meets

C A

produced in

D .

If

A B = 12, A C = 16, B C = 20,

then

B D =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 12

In a

∆ A B C,

the median

A D

is perpendicular to

A C .

If

b = 5

and

c = 11,

then

a =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 13

△ A B C

is an equilateral triangle where

A B = a

and

P

is any point in its plane such that

P A = P B + P C .

Then

\frac{P A^{2} + P B^{2} + P C^{2}}{a^{2}}

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 14

Let

a, b, c

be the sides of a triangle

A B C

such that

a = 2 c, \cos (A - C) + \cos B = 1

. Then the value of

C

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 15

If

A, B, C

are the angles of a triangle such that

\sin^{2} A + \sin^{2} B = \sin^{2} C,

then

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 16

In

∆ A B C, ∠ C = 2 ∠ A

and

A C = 2 B C

. Then which the following is/are true