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

In ΔABC, if b=c=R then A=

A.  300

B.  600

C.  900

D.  1200

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

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

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

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

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

A.  5

B.  12

C.  13

D.  13/2

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

A.  isosceles

B.  equilatcral

C.  right angled

D.  none

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

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

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

A.  600

B.  300

C.  900

D.  none

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

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

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)

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

In ΔABC, (r1 +r2) (r2 +r3) (r3+r1) =

A.  4Rs2

B.  4Rr2

C.  R

D.  0

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

A.  2√3

B.  √21

C.  8

D.  14

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

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)

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

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

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

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

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

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

A.  2

B.  √3

C.  2√3

D.  √2

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

A.  0

B.  1

C.  1/2

D.  2

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

A.  Δ

B.  3Δ

C.  2Δ

D.  4Δ

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

A.  right angled

B.  equilateral

C.  isosceles

D.  none

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

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