Question

EXPLANATION REQUIRED:
If angles A,B and C of a triangle are in AP and if a,b, c denote the length of the sides opposite to A,B and C resp. Then the value of the expression (a/c)sin2C+(c/a)sin2A is?

Answer 1

well if they form an A..P with common difference d ,then they will have to satisfy the following when

(x)+(x+d)+(x+2d)=180

where the terms in brackets are angles

Answer 2

i got x=60
but how to find 'd'?

Answer 3

how you got x=60 ?

Answer 4

3x+3d=180
then divide both the sides by 3

Answer 5

here's what i did
THE ANGLES ARE:
A
B=A+d
C=B+d
whee A.B.C are in ap.

now A+B+C=180
3A+3d=180
A+d=60
B=60

Answer 6

what is meant by AP?

Answer 7

arithmetic progression.
where a series is given to you but the difference between any two consecutive numbers is the same.

Answer 8

thanks

Answer 9

does the poster of this question still need help?

Answer 10

yes..yes..

Answer 11

ok. are you familiar with side the ratios of the 30:60:90 triangle?

Answer 12

yup...

Answer 13

of so lets just take this bit by bit. so the fraction a/c can be re-written as what trigonometric identitiy?

Answer 14

remember SOH-CAH-TOA (if you've heard that before). you with me?

Answer 15

yh..yh.. so is it cot?

Answer 16

no. sorry, it said it was written in AP so C should be the 90 degree angle

Answer 17

ahhh, sorry about that, give me one sec

Answer 18

no problem. :)

Answer 19

oki... you want me to tell you c/a with respect to which angle?

Answer 20

sorry a/c

Answer 21

well, you could write it a few ways but lets start evaluating the first part of the question (a/c)sin2C

Answer 22

if you are familiar with side ratio of 30:60:90 you will that the side ratio will be 1:root 3: 2

Answer 23

yup

Answer 24

so a/c is 1/root 3. now we can have a square root as the denominator so we multiple the top and bottom by root 3 and get (root 3)/ 3

Answer 25

now we multiply that my the next term which is sin(2C). C is 90 degrees so 2C is 180. what is the sin180?

Answer 26

0

Answer 27

yup, sorry for the delay, answering a physics question

Answer 28

0+root 3 sin60=2

Answer 29

c/a = 2

Answer 30

sin2A = Sin 60= 1/2

Answer 31

so (c/a)(sin60) = (1/2)(2)= 1

Answer 32

sin60=root3/2

Answer 33

you're right, i was looking at something else, i feel dumb.

Answer 34

thats okay..

Answer 35

so (1/2)(root3 / 2)

Answer 36

good?

Answer 37

but the answer is 2

Answer 38

are you telling me or asking me?

Answer 39

telling..

Answer 40

a/c=1/root 3
and c/a =root3
thats how you get two....