C2 The Sine and Cosine Rules

Question 1

The sine rule:

Answer 1

a/sin(A) + b/sin(B) + c/sin(C)
or
sin(A)/a + sin(B)/b + sin(C)/c

Question 2

The cosine rule:

Answer 2

a^2 = b^2 + c^2 - 2bccos(A)
or
cos(A) = (b^2 + c^2 - a^2)/(2b*c)

Question 3

Things to consider when using bearings:

Answer 3

• The angle is measured from North, not any lines that may be connected
• You must write angles with three digits, 039° not 39°

Question 4

Where do a,b,c,A,B & C go on a triangle when using the sine and cosine rules?

Answer 4

• A,B & C denote the angles at each of the vertices
• a,b & c are the lengths of each the triangle’s sides
• Lowercase and uppercase letters must be on opposite sides of the triangle
• It doesn’t matter which letters you assign to which sides/ angles so long as the above conditions are met, this makes life easier as you don’t generally have to rearrange the sine and cosine rules to use them, just label the triangle to fit the question

Question 5

What formula other than Area = 1/2baseheight can be used to calculate the area of a triangle?

Answer 5

1/2ab*sin(C)

Question 6

When should you use the sine rule to find an unknown length?

Answer 6

When you have two angles and the length of one of their opposite sides.

Question 7

When should you use the sine rule to find an unknown angle?

Answer 7

When you have the lengths of two sides and one of their opposite angles.

Question 8

When should you use the cosine rule to find an unknown length?

Answer 8

When you have the lengths of two sides and the angle between them.

Question 9

When should you use the cosine rule to find an unknown angle?

Answer 9

When you know the lengths of all three of the triangle’s sides.