Eamcet - Maths - Solutions Of Triangles

If, in aΔABC, r3=r1+r2+r , then ‹A+‹B is equal to

A.  1200

B.  1000

C.  900

D.  800

View Answer  

In ΔABC, if b=c=R then A=

A.  300

B.  600

C.  900

D.  1200

View Answer  

In ΔABC, if r1,r2,r3 are in H.P, then a, b, c are in

A.  A.P

B.  G.P

C.  H.P

D.  none

View Answer  

I: In a ΔABC, if 4s(s-a) (s-b) (s-c) =a2b2 then it is right angled triangle II: In a ΔABC, if sin A+ sin B +sin C maximum then triangle is equilateral

A.  only I is true

B.  only II is true

C.  both I,II are true

D.  neither I and II is true

View Answer  

In ΔABC, if cos A cos B +sin A sin B sin C =1, then a:b:c =

A.  1:1:1

B.  1:2:√2

C.  1:2:2

D.  1:1:√2

View Answer  

If 4,5 are two sides of a triangle and the included angle is 600, then is area is

A.  3

B.  5

C.  5√3

D.  3√3

View Answer  

In ΔABC, if r1 =3, r2= 10, r3= 15, then c=

A.  5

B.  12

C.  13

D.  13/2

View Answer  

.In ΔABC, if 2R+ r= r1, then the triangle isa

A.  isosceles

B.  equilatcral

C.  right angled

D.  none

View Answer  

If sin(y+z-x),sin(z+x-y), sin(x+y-z) are in A.P then tan x, tan y, tan z are in

A.  A.P

B.  G.P

C.  H.P

D.  A.G.P

View Answer  

If Two angles of a triangle are 300, 450 and the included side is √3+1, then the remaining sides are

A.  2,√2

B.  2,2√3

C.  √2,4

D.  2,4√3

View Answer  

In ΔABC, if (a+b-c) (a+b-c) = 3ab, then C =

A.  600

B.  300

C.  900

D.  none

View Answer  

In ΔABC, if a= 26, b=30, cos C=63/65 then  r1:r2:r3 =

A.  4:12:1

B.  3:4:12

C.  1:4:12

D.  4:12:3

View Answer  

In ΔABC, if a,b,c are in A.P. the greatest angle is A and least is C then 4(1- cos A) (1-cos C) =

A.  cos A + cos C

B.  cos A – cos C

C.  sin A + sin C

D.  cos A – sin C

View Answer  

If a, b, c are the sides of a triangle then the range of ab+bc+ca/a2+b2+c2 is

A.  [1, 2]

B.  (1/2, 1]

C.  [1/2, 2)

D.  (-1/2, 2)

View Answer  

If (a+b)2 = c2+ab in a ΔABC and if √2 (sin A+ cos A) =√3 then ascending order of angles A,B,C is

A.  A, B, C

B.  A, C, B

C.  B, A, C

D.  C, B, A

View Answer  

In ΔABC, (r1 +r2) (r2 +r3) (r3+r1) =

A.  4Rs2

B.  4Rr2

C.  R

D.  0

View Answer  

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

A.  2√3

B.  √21

C.  8

D.  14

View Answer  

If α, β are solutions of a tan θ+b sec θ=c then tan (α+β) =

A.  2ac/a2-c2

B.  2ac/c2-a2

C.  2ac/a2+c2

D.  none

View Answer  

If I1,I2,I3 are excentres of the triangle with vertices (0,0), (5,12), (16,12) then the orthocentre of ?I1,I2,I3 is

A.  (6,9)

B.  (7,9)

C.  (6,7)

D.  (9,7)

View Answer  

An observer finds that the angular elevation of a tower is θ. On advancing ‘a’ metres towards the tower, the elevation is 450 and on advancing b metres the elevation is 900-θ. The height of the tower is

A.  ab/(a+b)metres

B.  ab/(a-b)

C.  (a-b)/ab

D.  (a+b)/ab

View Answer  

A vertical tower stands on a declivity which is included at 150 to the horizon. From the foot of the tower a man ascends the declivity for 80 feet and then finds that the tower subtends an angle of 300. The height of the tower is

A.  20 (√6 - √2)

B.  40 (√6 - √2)

C.  40 (√6 + √2)

D.  none

View Answer  

In ΔABC , if c2= a2+b2, 2s= a+b+c, then 4s (s-a) (s-b) (s-c) =

A.  s4

B.  b2c2

C.  c2a2

D.  a2b2

View Answer  

In a triangle ABC, if cot A = (x3+x2+x)1/2, cot B= (x+x-1+1)1/2 and cot C= (x-3+x-2+x-1) -1/2 then the triangle is

A.  isosceles

B.  obtuse angled

C.  right angled

D.  none

View Answer  

If A=(1,1) ,B=(4,5) and C=(6,13) then cos A=

A.  64/63

B.  63/65

C.  56/36

D.  36/56

View Answer  

In ΔABC , if A=750, B=450, C=√3, then b=

A.  2

B.  √3

C.  2√3

D.  √2

View Answer  

In ΔABC, if a(b cos C + c cos B) =2ka2, then k =

A.  0

B.  1

C.  1/2

D.  2

View Answer  

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

A.  Δ

B.  3Δ

C.  2Δ

D.  4Δ

View Answer  

In ΔABC, if cos2 A+cos2B+ cos2C=3/4, then the triangle is

A.  right angled

B.  equilateral

C.  isosceles

D.  none

View Answer  

The angle of elevation of the summit of a mountain at a point A is 450. After walking 200 mt from A towards the mountain along a road included at 150, it is observed that the angle of elevation of the summit is 600. The height of the mountain is

A.  100 (√6 +√2) mt

B.  100 (√6 -√2) mt

C.  100/√6 mt

D.  100/√2 mt

View Answer  

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

A.  A.P

B.  H.P

C.  G.P

D.  none

View Answer