How Do You Find the Area of a Triangle Using ½ab Sin C?

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This formula applies when you know two sides and the angle directly between them. It comes from the standard triangle area formula $A=\frac{1}{2}\times \text{base}\times \text{height}$. If side $a$ is the base, the perpendicular height is $b\sin C$. Therefore,

Worked Example

A triangle has sides $8\text{ cm}$ and $11\text{ cm}$, with an included angle of $37^\circ$. Write the expression before using the GDC:

Using degree mode,

Therefore, the area is $26.5\text{ cm}^2$, correct to three significant figures. Keep the unrounded value stored on the GDC until the final answer.

Common Misconception

A common misconception is that any known angle can be used as $C$. This is incorrect: the angle must be directly between the two sides substituted as $a$ and $b$. If the known angle is not between those sides, first use another trigonometric relationship, such as the sine rule or cosine rule, to find suitable information.

Also ensure that the GDC is in degree mode when the angle contains a degree symbol. At HL, questions may instead use radians, so follow the unit stated in the question.

IB Exam Technique

This is SL 3.2-2D and 3D trigonometry, studied by both SL and HL students. For the command term calculate, show the formula and substitution before the GDC result, include square units, and normally give the final answer exactly or to three significant figures unless instructed otherwise.