Area of Triangle (SAS)
Find a triangle's area from two sides and the angle between them
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Bounded Oscillatory Function: Sine and cosine oscillate smoothly between -1 and +1 with period 360° (2π rad).
Variable Mechanics
Roles, constraints & impacts
Side a
Formula Parameter
Side b
Formula Parameter
Included Angle
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Bounded Oscillatory Function: Sine and cosine oscillate smoothly between -1 and +1 with period 360° (2π rad).
Common Mistakes & Traps
- Using Degree mode when Radians are expected (or vice versa).
- Tangent asymptotes at 90° and 270° (division by cos θ = 0 causes undefined infinity).
- Forgetting inverse trigonometric domain limits (e.g., arcsin input must be between -1 and 1).
Dimensional Analysis & Units
Ratio of side lengths → Dimensionless Scalar [-1, +1]
Real-World & Industry Application
Audio sound wave synthesis, AC alternating current electrical waveforms, robotic arm joint kinematics, and astronomical navigation.
Worked Example: Area of Triangle (SAS)
Given:
- a = 5
- b = 7
- C = 45
- A = ½ab·sin(C)
- A = ½(5)(7)·sin(45°)
- A = 17.5 × 0.7071
- A = 12.37 square units
Answer: 12.37
Frequently Asked Questions
What is the Area of Triangle (SAS) formula?
A = ½ab·sin(C). Find a triangle's area from two sides and the angle between them.
How do I calculate Area of Triangle (SAS)?
Enter Side a (a), Side b (b), Included Angle (C) into the calculator. It applies A = ½ab·sin(C) and shows every step of the working.
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