In the Sine Rule formula a/\sin(A) = b/\sin(B) = c/\sin(C), what do the letters *a*, *b*, and *c* represent?

The sides opposite to the angles

The sides adjacent to the angles

The sides opposite to the angles

Sine Rule

Q: When should you use the sine rule?

Use the sine rule on a triangle that is not right-angled, when you need to find a missing side or angle. You must know at least one complete pair: an angle together with the length of the side directly opposite it. That single pair is enough to start.

Q: What is the sine rule formula?

The sine rule says each side divided by the sine of its opposite angle gives the same value, so a / sin A = b / sin B = c / sin C. You can turn every fraction upside down to get sin A / a = sin B / b = sin C / c.

Q: How do you find a missing angle using the sine rule?

Set the sine rule up with the sines on top rather than the sides. Work out the sine of the angle you already know, then cross-multiply and divide to find the sine of the missing angle. Finally, apply the inverse sine function to that value to get the angle.

Key concept

The Sine Rule is a/sin A = b/sin B = c/sin C. It finds a missing side or angle in a non-right-angled triangle, linking each side to its opposite angle. You just need one angle and its opposite side as a matching pair.

Video Lesson

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$Sine Rule poster$

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Flashcards

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Sine Rule Formulas for finding missing sides or angles.

Sine Rule applied to a triangle with angles 30°, 70°, and one unknown angle, showing how to find the opposite side of 4 cm using the sine rule.

Applying the sine rule to find angles with a triangle, with the equation sin(135°)/10 cm = sin(theta)/5 cm.

What Is the Sine Rule?

The Sine Rule is used to find missing sides or angles in a non-right-angled triangle.
The formula is $\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}$ .

Practice Questions

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Q1Easy

What information is required to apply the Sine Rule?

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Interactive Activity

Drag Point B to generate new practice problems

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Find Side

Step 1: Use the Known Pair

We know Angle A and Side a.

Step 2: Set up Equation

Equate it to Pair B to find b.

Step 3: Solve

b =

10.0

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Students Also Ask

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When should you use the sine rule?

Use the sine rule on a triangle that is not right-angled, when you need to find a missing side or angle. You must know at least one complete pair: an angle together with the length of the side directly opposite it. That single pair is enough to start.

What is the sine rule formula?

The sine rule says each side divided by the sine of its opposite angle gives the same value, so a / sin A = b / sin B = c / sin C. You can turn every fraction upside down to get sin A / a = sin B / b = sin C / c.

How do you find a missing angle using the sine rule?

Set the sine rule up with the sines on top rather than the sides. Work out the sine of the angle you already know, then cross-multiply and divide to find the sine of the missing angle. Finally, apply the inverse sine function to that value to get the angle.

Why can you turn the sine rule formula upside down?

Because each side and the sine of its opposite angle keep the same ratio, the equation stays true whether the sides sit on top or the sines do. Writing the sides on top makes a missing side easier to find, while the sines on top suit a missing angle.

Do you need to label the sides and angles to use the sine rule?

No. The sine rule does not need you to label every angle and side first. You only have to spot one pair where you know an angle and the length of the side directly opposite it. Once you have that pair, you can set up the rule and solve.

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