Area of Triangle with Sine
Area from two sides and the included angle.
Key idea
Area from two sides and the included angle.
In depth
A = ½ab sin C, where C is the angle between sides a and b. It replaces base × height when the height is unknown, since the height is b sin C.
Worked example
Sides 6 and 8 with a 30° angle between them: A = ½ × 6 × 8 × 0.5 = 12.
Formula
Real-world uses
- Finding the area of a triangular field from two sides and the angle between them
Common mistake
Using an angle that is not between the two sides.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Area of Triangle with Sine?
Area from two sides and the included angle. It is a topic at the advanced level in Trigonometry.
What is the formula for Area of Triangle with Sine?
The key formula is A = ½ ab sinC.
Where is Area of Triangle with Sine used in real life?
Real-world examples: Finding the area of a triangular field from two sides and the angle between them.
What should I learn before Area of Triangle with Sine?
Make sure you are comfortable with Law of Cosines, the previous topic in Trigonometry.
What is a common mistake with Area of Triangle with Sine?
Using an angle that is not between the two sides.
How can I practise Area of Triangle with Sine?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Area of Triangle with Sine?
Move on to Bearings and Navigation next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.