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Sine Rule

​Purpose

The Sine Rule (or Law of Sines) is used to solve triangle angles or sides when there is no right angle.

Specifically, the Sine Rule is applied when given information relates to two pairs of angles with their opposite sides.

The Sine Rule is based on a conventional arrangement of labels on the diagram of a triangle.
Note: an angle and opposite side are a matching upper and lower case letter. This pairing is important.

​

​Convention

Sine rules

The sine rule is used when we are given either

a)two angles and one side,

b) two sides and a non-included angle

​Statement of the Sine Rule

​The next three slides will take you to Khan Academy video example and a short quiz with access to support. When done, come back to this Quizizz task tab to continue.

Law of sines: solving for a side | Trigonometry (video) | Khan Academy

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Law of sines: solving for an angle | Trigonometry (video) | Khan Academy

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Solve triangles using the law of sines (practice) | Khan Academy

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Multiple Choice

Find the value of a.

• 13.4

• 12.9

• 13.0

• 12.8

Multiple Choice

Find the value of b.

• 19.3

• 20.0

• 18.5

• 19.0

Multiple Choice

Find the value of c.

• 19.4

• 31

• 15.2

• 24.2

Multiple Choice

Find the value of c.

• 24.7

• 28.2

• 23.4

• 25.3

Multiple Choice

Find the size of angle X.

• 0.6

• 36.2

• 36.9

• 36.4

Multiple Choice

Find the missing angle θ

• 27.98^o

• 29.24^o

• 26.75^o

• 45^o

Multiple Choice

Find the missing side x

• 6.65cm

• 1.74cm

• 5.66cm

• 7.14cm

Multiple Choice

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them.  THe angle of elevation from Amanda to the bird is 55, and from Jamie tot he bird is 63.  How far away is the bird from Amanda?

• 25.23
• 23.19
• 22.15
• 20.85

Multiple Choice

When using the sine rule how many parts (fractions) do you need to equate?

• All 3 parts
• 1 part
• 2 parts

Multiple Choice

In triangle ABC shown below, AC = 14 km, AB = 28 km and angle ACB = 87 degrees. Select one of the following that can be used to find angle B

• $$\frac{28}{Sin\ B}\ =\ \frac{14}{Sin\ \ 87}$$

• $$\frac{87}{Sin\ B}\ =\ \frac{14}{Sin\ \ 28}$$
  

• $$\frac{14}{Sin\ B}\ =\ \frac{28}{Sin\ \ 87}$$
  

• $$\frac{B}{Sin\ 28}\ =\ \frac{87}{Sin\ \ 14}$$