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

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Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20)
Properties of Triangle Questions With Solutions (Q.No. 21 To Q.No 40)
Properties of Triangle Q. No. 41 to 60
Properties of Triangle Q. No. 61 to 80
Properties of Triangle Q. No. 81 to 100

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:

$\sqrt{3}$

B. $\sqrt{6}$

C. 3

D. $1+\sqrt{2}$

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 $\frac{1}{\sqrt{A_{1}}}+\frac{1}{\sqrt{A_{2}}}+\frac{1}{\sqrt{A_{3}}}=$

Options:

A. $\frac{3}{\sqrt{A}}$

B. $\frac{2}{\sqrt{A_{1}}}$

C. $\frac{1}{\sqrt{A}}$

D. $\frac{1}{\sqrt{A_{1}A_{2}A_{3}}}$

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, $\frac{sinA}{4}=\frac{sinB}{5}=\frac{sinC}{6}$ , 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 = $\sqrt{3}$ cm and angle A = $\pi$ /6, then find distance between its circumcentre and incentre

Options:

A. 2 + $\sqrt{3}$

B. $\sqrt{2+\sqrt{3}}$

C. $\sqrt{2-\sqrt{3}}$

D. 2 – $\sqrt{3}$

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:

Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20)
Properties of Triangle Questions With Solutions (Q.No. 21 To Q.No 40)
Properties of Triangle Q. No. 41 to 60
Properties of Triangle Q. No. 61 to 80
Properties of Triangle Q. No. 81 to 100

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. $\sqrt{13}$ /12

B. 3 $\sqrt{13}$ /12

C. 5 $\sqrt{13}$ /12

D. 7 $\sqrt{13}$ /12

Solution:

Ques No 32:

If $\alpha, \beta, \gamma$ are the distance of the vertices of a triangle from the corresponding point of contact with the incircle, then the value of $\alpha\beta\gamma/(\alpha+\beta+\gamma)$ 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, $\sqrt{a^{2}+2ab+b^{2}}$ , 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 $\frac{a(cosB+cosC)}{(b+c)sin^{2}(A/2)}$ is

Options:

A. 1

B. 4

C. 3

D. 2

Solution:

Ques No 40:

In a triangle ABC, the value of $\frac{tan\frac{A}{2}+tan\frac{B}{2}}{tan\frac{A}{2}-tan\frac{B}{2}}$ is

Options:

A. (a + b)/c

B. c/(a – b)

C. c/(a + b)

D. (a – b)/c

Solution:

Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20)
Properties of Triangle Questions With Solutions (Q.No. 21 To Q.No 40)
Properties of Triangle Q. No. 41 to 60
Properties of Triangle Q. No. 61 to 80
Properties of Triangle Q. No. 81 to 100

Trigonometry Properties Of Triangle Questions With Solutions Q No 21 To 40

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

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

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