0
Imagine a random triangle ABC. It will make it easier if you draw it with angle C at the top. The opposite side of angle A is labelled a, the opposite side of angle B is labelled b and the opposite side of angle C is labelled c. Draw the altitude (height) from angle C so that it is perpendicular (at 90 degrees) to side c.
Looking at this triangle, find expressions for the sines of angles A and B:
sinA = h/b
sinB = h/a
Rearrange these two equations in terms of h:
h = bsinA
h = asinB
As h = h, these equations can be set equal to each other and simplified to find the sine rule:
bsinA = asinB
sinA/a = sinB/b
If you expand on this way of working, you can also find that sinA/a = sinB/b = sinC/c. You have now proven the sine rule for all triangles!
Still curious? Ask our experts.
Chat with our AI personalities
Devin
Rene
BeauAdd your answer:
Earn +20 pts
Is it is necessary to be a right angle triangle to use sine rule?
No. Sine rule (and cosine rule) apply to all triangles in Euclidean space (plane geometry). A simplification occurs when there is a right angle because the sine of the right angle is 1 and the cosine is 0. Thus you get Pythagoras theorem for right triangles.
What is the length of the side of a triangular fence if one side is 100 feet and the other side is 200 feet?
Use the sine rule to find the the length of third side. Sine rule: a/sinA = b/sinB = c/sinC
What proportion do you use to find the length of the third side triangle XYZ?
The answer depends on the information that you have: it could be the sine rule or the cosine rule.
What theorem states that if three forces acting at a point they are in equilibrium then each force is proportional to the sine of the angle between the other two?
The result is a direct consequence of the sine rule.
How do you find the leg of a triangle with no right angles?
By using the Sine rule: a/sinA = b/sinB = c/sinC
