Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 150 off

				   what is sine rule?

7 years ago


Answers : (4)



The Sile rule or the law of sines states that, for any triangle ABC,

sin(A)/a = sin(B)/b = sin(C)/c,

where A,B and C are the angles of the triangles and a,b,c are the lengths of the sides opposite to each of these angles.

This allows us to work out any length and angle that we don't know, provided we do know some of the lengths and angles in the triangle.

An example :

Suppose we know that angle A in the triangle above is 45o, that angle B is 30o and that the length b is 2 units.

We know that angle A in the triangle above is 45o, that angle B is 30o and that the length b is 2 units.

To work out the remaining angle, we need to remember that the angles within a triangle always add up to 180o.

Since we know A and B add up to 75o, the angle C must be 105o.

Now to find the length a, we can use the first part of the sine rule above. We can rearrange a/sinA = b/sinB to get a=bsinA/sinB.

Since we know A and B we can evaluate this expression to get


Finally we can use the second part of the sine rule to find the length c:

b/sinB=c/sinC, so c=bsinC/sinB

That gives c=2sin(105o)/sin(30o)

which is 4sin(105o).

We can write sin(105o) as sin(150o-45o) then use the sin(A-B) rule to write this as


Putting in the values for the sine and cosine of these special angles gives



7 years ago


Sine Rule

Case 1 (If A is an acute angle)

Consider angle A

Now      ÐBAC = ÐBPC (Ðs in same segment)

          sin A = sin ÐBPC 

but        ÐBPC = BC/BP

                   = a/2R

           sin A = a/2R

              2R = a/sin A



Case 2 (If A is an obtuse angle)

Now  ÐBAC + ÐBPC = 180° (opp.  of cyclic quad.) 

                    ÐBAC = 180° - ÐBPC 

               sin ÐBAC = sin (180° - ÐBPC

                            = sin ÐBPC

               sin ÐBPC = BC/BP

                            = a/2R

                    sin A = a/2R 

                        2R = a/sin A


Similarly, by considering ÐB and ÐC, it can be proved that


where b = AC, the side opposite angle B, and c = AB, the side opposite angle c.




This rule can also be used in this format


7 years ago

SinA/a = SinB/b = SinC/c


this is sine  rule where A B C are angles of triangles and a b c are are opposite sides

6 years ago

its used for relating sides and angles of a triangle

it states that side a/sin A =side b/sin B =side c/sin c

6 years ago

Post Your Answer

Other Related Questions on Trigonometry

let g(x)=ax+b,where a
Dear Swati, Your question-------> let g(x)=ax+b,where a is incomplete. Please post it again. Best of luck!
Vikas TU one month ago
let a,b,c be the sides oppositwe the angles A,B,C of triangle ABC.find the value of k a+b=ck
refer R.D. sharma Book there you will find all the answers of your queries. its the best book for all the geometric questions
aadish jain one month ago
if a=cosϴ + i sinϴ , find the value of 1+a/1-a?????????????????????????????????????????
hey, a=cosϴ + i sinϴ (given)
Nishant Vora one month ago
i am facing problems in solving questions from topic quadratic equations .from which book should i study the topic?
Hii You can go for Arihant books or TMH for practising questions of Quadratic eqns
Sourabh Singh 2 months ago
@ tanbro what u can do is frst brush up your besics from ncert , then move ahead , after that take math by m l khanna and problems in maths by a dasgupta ,, they have explained each and...
Umakant biswal 2 months ago
Arihant book on algebra will give good variety of question similar to what is asked in JEE . The book also have sufficient theory to get you started. Higher algebra by hall and knight is...
Ajay 2 months ago
The extremities of the base of an isosceles triangle ABC are the points A(2,0) and b (0,1).if the equation of the side ac is x=2 then the slope of the side bc is???
equation of side ac is x=2, so the point c has coordinates (2,k) and also distance between points a and c is equal to points b and c(since isosceles),so (k=5/2) and usng slope formula slope ...
arunkumaran 26 days ago
What is the parallelogram law of two vectors and what is definations of dot product and cross product
Acccording to the parallelogram law of vector addition: "If two vector quantities are represented by two adjacent sides or a parallelogram. then the diagonal of parallelogram will be equal...
KALYAN 10 months ago
HELLO PRABHAKAR parallelogram law of vector addition states that when two vectors are represented by two adjacent sides of a parallelogram by direction and magnitude then the resulatant of...
raj 9 months ago
in parallelogram of vectors two vectors are represented by two adjacent sides in parallelogram of vectors the square of the diagonal is equal to squre root of two adjacent sides squares and ...
RAMCHANDRARAO 9 months ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 150 off

More Questions On Trigonometry

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details