Solution of Triangles

Solution of Triangles

The Sine Rule

• The sine rule is an equation that can help you find missing sides or angles in any triangle.
• It is written as a/sin(A) = b/sin(B) = c/sin(C).
• To find a missing side, rearrange the formula to a = b * sin(A)/sin(B).
• To find a missing angle, rearrange the formula to A = arcsin[a * sin(B)/b].

The Cosine Rule

• The cosine rule is another equation that can help you find missing sides or angles in any triangle.
• It is written as c^2 = a^2 + b^2 - 2ab*cos(C).
• To find a missing side (c), simply plug the known values into the formula.
• To find a missing angle (C), rearrange the formula to C = arccos[(a^2 + b^2 - c^2) / 2ab].

Area of a Triangle

• The formula for the area of a triangle when you know two sides and the included angle is 1/2ab*sin(C).
• This is a key formula and often used in conjunction with the sine or cosine rules.

Handling the Ambiguous Case

• Sometimes, using the sine rule can produce two possible values for a missing angle, known as the ambiguous case.
• Always check for this by seeing if sin(A) is less than or equal to the length of the other known side.
• If it is, there are two possible solutions. If not, there is only one.

Remember, it’s not just about memorising these formulas but understanding when to use them. Practice is key, so use past paper questions to apply these rules in different contexts.