Trigonometry Properties of Triangle Questions With Solutions Q No 21 to Q No 40

In this post, you will get some important Trigonometry Properties of Triangle Questions with Solutions Q No 21 To Q No 40. Questions will be solved soon.

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Ques No 21:

If acosA = bcosB in triangle ABC, then the angle C is

Options:

A. 45 degree

B. 60 degree

C. 90 degree

D. None Of These

Solution:

Ques No 22:

In triangle ABC, if a = 2, B = 60 degree and C = 75 degree, then the value of b is

Options:

A. 

B. 

C. 3

D. 

Solution:

Read : Trigonometric Conditional Identities Important Questions

Ques No 23:

If A, A1, A2, A3 are the areas of incircle and excircles of a triangle, then 

Options:

A. 

B. 

C. 

D. 

Solution:

Ques No 24:

In triangle ABC, acosA + bcosB + ccosC is

Options:

A. r + R

B. r – R

C. 2(r + R)

D. 2(r – R)

Solution:

Ques No 25:

If in a triangle, the ex-radii r₁, r₂, r₃ are in the ratio 1 : 2 : 3, then the sides of the ratio is

Options:

A. 5 : 8 : 9

B. 1 : 2 : 3

C. 3 : 5 : 7

D. 1 : 5 : 9

Solution:

Ques No 26:

If in a triangle, the base of the length of a and the ratio of two sides is r (r < 1), then the maximum value of the altitude is

Options:

A. ar

B. ar/(1 + r²)

C. ar/(1 – r²)

D. a/r

Solution:

Ques No 27:

If in a triangle ABC, , then the value of cosA + cosB + cosC is

Options:

A. 1/48

B. 69/48

C. 50/69

D. None of these

Solution:

Read : Trigonometric Maximum & Minimum Important Questions

Ques No 28:

In a right angled triangle ABC, cos²A + cos²B + cos²C is

Options:

A. 0

B. 1

C. -1

D. None of these

Solution:

Ques No 29:

In a triangle ABC, if b = 2 cm, c =  cm and angle A = /6, then find distance between its circumcentre and incentre

Options:

A. 2 + 

B. 

C. 

D. 2 – 

Solution:

Ques No 30:

If x, y and z are respectively be the perpendicular from the circumcentre to the sides of triangle ABC, then the value of a/x + b/y + c/z is

Options:

A. (abc)/(xyz)

B. (abc)/(2xyz)

C. (abc)/(3xyz)

D. (abc)/(4xyz)

Solution:

Ques No 31:

In a triangle ABC, a = 5, b = 4, C = 3, G is the centroid of triangle, then the value of circumradius of triangle GAB is 

Options:

A. /12

B. 3/12

C. 5/12

D. 7/12

Solution:

Ques No 32:

If  are the distance of the vertices of a triangle from the corresponding point of contact with the incircle, then the value of  is 

Options:

A. r

B. r²

C. 1/r

D. 1/r²

Solution:

Ques No 33:

If the median AD of a triangle ABC is perpendicular to AB, then the value of tanA + 2tanB is

Options:

A. 0

B. 1

C. -1

D. 2

Solution:

Ques No 34:

In a triangle ABC, if a, b, c are in AP, then find the value of tan(A/2)tan(C/2).

Options:

A. 1/4

B. 1/3

C. 1/2

D. 1/5

Solution:

Ques No 35:

In a triangle ABC, if bsinC(b cosC + c cosB) = 42, then the area of the triangle ABC is

Options:

A. 21 sq. units

B. 42 sq. units

C. 20 sq. units

D. None of these

Solution:

Read : Trigonometric Allied Angles Important Questions

Ques No 36:

In a triangle ABC, if b = 3, c = 5 and cos(B – C) = 7/25, then find the value of tan(A/2).

Options:

A. 1/3

B. 1/4

C. 1/2

D. None of these

Solution:

Ques No 37:

In a triangle ABC, x = tan{(B – C)/2}tan{A/2}, y = tan{(C – A)/2}tan{B/2}, z = tan{(A – B)/2}tan{C/2}, then 

Options:

A. x + y + z = 0

B. x + y + z = -xyz

C. x + y + z = xyz

D. None of these

Solution:

Ques No 38:

The sides of a triangle ABC are a, b, , then the greatest angles of the triangle ABC is 

Options:

A. 135 degree

B. 105 degree

C. 120 degree

D. 150 degree

Solution:

Ques No 39:

In a triangle ABC, the value of  is

Options:

A. 1

B. 4

C. 3

D. 2

Solution:

Ques No 40:

In a triangle ABC, the value of  is

Options:

A. (a + b)/c

B. c/(a – b)

C. c/(a + b)

D. (a – b)/c

Solution: