Trigonometry Properties of Triangle Questions With Solutions Q No 01 to Q No 20

In this post, you will get some important Trigonometry Properties of Triangle Questions with Solutions Q No 01 To Q No 20. Questions will be solved soon.

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Ques No 1:

In triangle ABC, if  and a = 2, then area of triangle ABC is

Options:

A. 1

B. 2

C. 

D. 

Solution:

Ques No 2:

In triangle ABC, if a = 4, b = 3, angle A = 60 degree. then c is a root of the equation

Options:

A. c² – 3c – 7 = 0

B. c² + 3c + 7 = 0

C. c² – 3c + 7 = 0

D. c² + 3c – 7 = 0

Solution:

Read : Trigonometric Inequalities Important Questions

Ques No 3:

In cotA/2 = (b + c)/a, then the triangle ABC is

Options:

A. Isosceles Triangle

B. Equilateral Triangle

C. Right Angled Triangle

D. None of These

Solution:

Ques No 4:

In triangle ABC, sin²A + sin²B + sin²C is

Options:

A. 0

B. 1

C. -1

D. 2

Solution:

Ques No 5:

In c² = a² + b², 2s = a + b + c, then 4s(s – a)(s – b)(s – c) is

Options:

A. s⁴

B. b²c²

C. c²a²

D. a²b²

Solution:

Ques No 6:

In an equilateral triangle, the inradius, circumcentre and one of ex-radii are in ratio

A. 2 : 3 : 5

B. 1 : 2 : 3

C. 1 : 3 : 7

D. 3 : 7 : 9

Solution:

Read : Trigonometric Multiple & Submultiple Angles Important Questions

Ques No 7:

In triangle ABC, , then the angle A is

A. 30 degree

B. 60 degree

C. 90 degree

D. 45 degree

Solution:

Ques No 8:

If in triangle ABC,  = a² – (b – c)², then tan(A/2)

A. 15/4

B. 1/4

C. 1/2

D. 1/5

Solution:

Ques No 9:

Point D, E are taken on the sides BC of triangle ABC such that BD = DE = EC. If angle BAD = x, angle DAE = y, angle EAC = z, then {sin(x + y)sin(y + z)}/(sin x sin z) is

A. 1

B. 2

C. 3

D. 4

Solution:

Ques No 10:

In triangle ABC, 3a = b + c, then find cot(B/2)cot(C/2)

A. 1

B. 

C. 2

D. None of These

Solution:

Ques No 11:

If A + B + C = , n  Z, then tan(nA) + tan(nB) + tan(nC) is equal to 

A. 1

B. 0

C. tan(nA)tan(nB)tan(nC)

D. None of These

Solution:

Ques No 12:

If triangle ABC, (b + c)/11 = (c + a) /12 = (a + b)/13, then cos A is 

A. 1/5

B. 5/7

C. 19/35

D. None of These

Solution:

Ques No 13:

If p₁, p₂, p₃ are altitude of triangle ABC from the vertices A, B, C and  be the area of the triangle, then p₁^-1 + p₂^-1 – p₃^-1 is

A. (s – a)/

B. (s – b)/

C. (s – c)/

D. s/

Solution:

Ques No 14:

In triangle ABC, angle A = 75, angle B = 75, then a + c is 

A. 0

B. b

C. 2b

D. -b

Solution:

Ques No 15:

If in triangle ABC, cos A = (sin B)/(2sin C), then triangle ABC is

A. Equilateral 

B. Isosceles

C. Right Angled 

D. None of These

Solution:

Ques No 16:

If r, r₁, r₂, r₃ are radius of incircle and excircle, then the value of 1/r₁ + 1/r₂ + 1/r₃ is

A. 1

B. 0

C. 1/r

D. None of These

Solution:

Read : Trigonometric Sum & Difference Angles Identities Important Questions 

Ques No 17:

If p₁, p₂, p₃ are altitude of triangle ABC from the vertices A, B, C to the opposite sides, then p₁p₂p₃ is

A. (a²b²c²)/R²

B. (a²b²c²)/4R²

C. (4a²b²c²)/R²

D. (a²b²c²)/8R²

Solution:

Ques No 18:

If exradii r₁, r₂, r₃ of triangle ABC are in HP then its sides are in 

A. AP

B. GP

C. HP

D. None of These

Solution:

Ques No 19:

In a triangle ABC, (1 – r₁/r₂)(1 – r₁/r₃) = 2, then the triangle is 

A. Right Angled

B. Isosceles

C. Equilateral

D. None of These

Solution:

Ques No 20:

The value of 1/r₁² + 1/r₂² + 1/r₃² + 1/r²  is 

A. 0

B. (a² + b² + c²)/²

C. ²/(a² + b² + c²)

D. (a² + b² + c²)/

Solution: