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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!
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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
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.
How does one differentiate between the sine rule and the cosine rule?
The sine rule is a comparison of ratios: (sin A)/a = (sin B)/b = (sin C)/c. The cosine rule looks similar to the theorem of Pythagoras: c2 = a2 + b2 - 2ab cos C.
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
How does one differentiate between the sine rule and the sine ratio?
The sine rule(also known as the "law of sines") is: a/sin A = b/sin B = c/sin C where the uppercase letters represent angles of a triangle and the lowercase letters represent the sides opposite the angles (side "a" is opposite angle "A", and so on.) Sine Ratio(for angles of right triangles): Sine of an angle = side opposite the angle/hypotenuse written as sin=opp/hyp.
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 prove sin90equalsto 1?
Make a diagram. One way to define sine and cosine is with the unit circle - a circle with a radius of 1 unit. For any point on the circle, the sine is the y-component, while the cosine is the x-component.
How do you find the leg of a triangle with no right angles?
By using the Sine rule: a/sinA = b/sinB = c/sinC
What are the answers to the my maths sine rule questions?
There are several websites that will help you cheat on homework and study assignments. This site is not one of them.
What is sine equation?
the sine rule, angle (a) and opposite length is eaqual to angle (b) and opposite length. which are also equal to angle (c) and opposite length. Sin A = Sin B = Sin C ------- -------- ---------- a -------- b -------- c
What is a mathematical rule called?
A mathematical rule can be called many things including a theory. Proofs can prove this theory to be a rule.
Can the law of cosines be used to find a length or just angle?
Either.However, if you know two sides and the includedangle then the sine rule is simpler.
