Sine & Cosine Rules

This lesson covers:

  1. How to use the Sine and Cosine rules to find missing sides or angles in triangles that do not have a right-angle
  2. Also known as the 'Law of Sines' and 'Law of Cosines' 

Video coming soon

Is the equation below a form of the sine rule or the cosine rule?

sin(A)a​=sin(B)b​

Sine rule

Cosine rule

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When do you use the sine rule?

In questions involving 3 sides and 1 angle

In questions involving 2 sides and 2 angles

In questions involving 1 side and 3 angle

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Is the equation below a form of the sine rule or the cosine rule?

a2=b2+c2−2bccos(A)

Cosine rule

Sine rule

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When do you use the cosine rule?

In questions involving 2 sides and 2 angles

In questions involving 3 sides and 1 angle

In questions involving 1 side and 3 angle

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Triangle with sides labeled 4.8 mm, 6.4 mm, and an angle of 123 degrees, with side x to be calculated.

Calculate the length of side x. Give your answer to 3 significant figures.

9.87

mm

mm

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Triangle with sides and angles labelled for calculating the length of side y using sine and cosine rules.

Calculate the length of side y. Give your answer to 2 decimal places.

4.34

cm

cm

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Triangle with sides 4 cm, 6 cm, and 8 cm, and angle x to be calculated.

Calculate angle x. Give your answer to 3 significant figures.

104

°

°

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Triangle ABC with angle measurements of 28 degrees at B, 134 degrees at C, and side BC measuring 10.2 cm.

Calculate the length of AC. Give your answer to 3 significant figures.

6.66

cm

cm

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Triangle problem showing sides of 5.2 cm and 6.7 cm with an angle of 117 degrees. Find the length of side x.

Find the length of side x. Give your answer to 3 significant figures.

10.2

cm

cm

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Triangle with sides 6.7 cm and 8.1 cm and angles 97 degrees and x degrees.

Find angle x. Give your answer to 3 significant figures.

55.2

°

°

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Triangle EFG with angles 73 degrees at E and 26 degrees at G, and side EG measuring 13.5 meters.

Calculate the length of EF. Give your answer to 3 significant figures.

5.99

m

m

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