can someone explain the law of sines?

Question

i am having a problem....i'm having a right angles triangle in which i know all the three angles and the base....how can i find the hypotenuse? i have heard that that this is possible thorugh the law of sines...how? what is this law? and what are sines?can someone please guide me?

Answer 1

Consider right angled triangle , right angled at B.
Hypotenuse is AC = h, say
BC = base = b
cos C = BC / AC
cos C = b / h
h cos C = b
h = b / cos C (so h can be found)

Answer 2

You need to pick up a trigonometry book. You can find at a library.

But here is some info.

In a right angle triangle biggest (longest) side is hypotenuse.

Sine of an angle = opposite side Divided by hypotenuse.
Co-sine of an angle = Adjutant side divided by hypotenuse.
Tangent of an angle = Opposite side divide by adjutant side.

Pythagoras theorem:

Square on the hypotenuse = Sum of the squares on the other two side.

Hint:

Now say angles are "C"= 90 degree, "A" degree and "B" degree.

By defination sine of 90 degree = oppositeside/Hypotanues but here opposite side is the hypotanues so, Sin90 =1

Base is the adjasent side in this case and we have said it is "b" unit (a known quantity). The other side "a" and the hypotenus is "c", so "a" & "c" are unknow all others thing are know.

In the book you will find Sine rule or Sine law, and it is,

Law of sines say
(a/sin A )= (b/sin B) = (c/sinC),

So,
c= (a*Sin C)/SinA, but sine of "C" = 1

c =

In the same book you can find the values of sine for different angles listed, so you can find the value for "c"

Answer 3

Law of sines says the ratio of the sine of an angle in a triangle to the length of the side facing opposite the angle is the same for all the angles.

Sine is a function of an angle. If you have a circle, and sweep out an angle along the circle, the sine is the y coordinate of where you stop, divided by the radius.

I guess they assume you can press the sine button on the calculator for this problem though.

Answer 4

length of the side opposite the angle divided by the sine of the angle is a constant.

so if you have a triangle with straight lines connecting points labelled A,B and C and angles a,b,c in the interior wedges of those points then if AC = length of line between point A and pointC : AC/sin(b) = AB/sin(c) = BC/sin(a)

so now let AC be the hypotenuse and BC be the base then
BC/sin(a)=hypotenuse/sin(90)=hypotenuse

Answer 5

Call the angles of the triangle, A, B and C.
Call the sides adjacent to these angles, a, b and c.
Now sine law says that:
a/sin(A) = b/sin(B) = c/sin(C)
Let C be 90 degrees. So 'c' is the hypotenuse.
You know three angles, A, B and C.
You know a side. Call it 'a'.
Find 'c' using the formula:
c=a*sin(C)/sin(A)
c=a/sin(A) (since C = 90 degrees and sin(90) = 1)
Thats it !

Answer 6

law of sines say
(a/sin A )= (b/sin B) = (c/sinC)
where A , B and C are the three angles and
a, b, and c are the opposite sides
so if you know all three angles and one side (say if you know side a and all angles A, B , C)
then side b = (a* Sin B)/Sin A
c= (a*Sin C)/SinA
regards
morgan
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Answer 7

measure the angle between perpendicular and hypotneuse and since sin Q = perpendicular/ hypotneuse , you can find the value of hypotneuse with the help of sine of that angle. If you don't have the value of perpendicular then you can take the base as perpendicular and the angle opposite to it as Q.

Answer 8

sin(x) = Perpendicular / Hypotenuse

cos(x) = Base/Hypotenuse

tan(x) = Perpendicular / Base.

where x is an angle (other than the right angle).
The side that is adjacent to this choosen angle is the Base, and opposite to the angle is the Perpendicular...

You can remember this formula using this line...
"Some People Have
Curly Black Hair
To Produce Beauty"

i.e., S = P/H; C = B/H; and T=P/B to get the above mentioned formula.

Answer 9

the rated of the length of the side opposite one of the angles
in a right -angled .triangle that are less then 90` to the length of the longest side compare...
kewal