1. In a triangle A=45degree. , B= 75 degree. Show that a+c root 2 =2b

2. In a triangle all angles are in AP and 2b² = 3c². Determine the value of angle A.

1.

sinA/a=sinB/b=sinC/c

sin(45)/a=sin(75)b=sin(60)/c

1/aroot2=(root3+1)/b=root3/2c

root2/a=(root3+1)/broot2=root3/c

a(root3)+a=2b ; a(root3)=c(root2)

a+c(root2)=2b

if wrong please correct me and tell me whether i am correct or not?

2.

let the angles be A-d,A,A+d

A-d+A+A+d=180(sum of the angles in a trinagle is 180)

3A=180

A=60degrees

if wrong correct me and tell me whether i am correct or not?

there is not even a single person to tell whether my answer is correct or not?

it is 3days past that i had answered this question.

CAN ANY ONE PLEASE RATE ME FOR THIS.PLEASE......................................................................................................................................................................................

Hello dear. u r right only 5 %. u do not use the condition 2b² = 3c²

u have to use this condition. Apply it the following way

2b = a+c 

at least tell about 1st question

well try  vnkt.swaroop ,

Dear REJAULMA,

I think a,b,c are the sides of triangle and Let A,B,C are the respective angles which are in AP

so 2B =A+C            and since A+B+C =180

hence 2B = 180-B

hence B=60

now apply Sin Rule:

SinB/b =Sin C/c

or Sin60 /b = Sin C/c

or sinC = c Sin60 /b

or sin² C = c² Sin²60 /b²  =3c²  /4b2

from given eq:  sin² C = 2b²/4b²

or sin² C = 1/2   or Sin C =1 / root(2)    =>   C =45

hence ,A = 75

hello dear.

obviously angle C = 180 - (75+45) = 180 - 120=60

now from the sine formula a/sin A = b / sin B = c / sin C , we can write

a/ sin 45 = b/ sin 75 = c / sin 60

a/ 1√2 = b / (√3 + 1)/2√2 = c / √3/2 = k (say)

Now , a + c √2 = k { 1/√2 + √3/2 * √2}

= k [ 1/√2 + √3/√2]

= k [ (1+√3) / √ 2]

= 2k [ (√3 + 1 ) / 2 √2]

= 2b.

ok dear