Solving Non-Right Triangles
The **Law of Sines** and the **Law of Cosines** are two powerful formulas used to solve for unknown sides and angles in **any** triangle, not just right triangles.
You use the **Law of Sines** when you have an angle and its opposite side (a complete ratio), plus one other piece of information. This includes Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and the sometimes tricky Side-Side-Angle (SSA).
$$ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} $$You use the **Law of Cosines** when you have no complete angle-side ratios. This includes Side-Side-Side (SSS) and Side-Angle-Side (SAS).
$$ c^2 = a^2 + b^2 - 2ab \cos(C) $$Score: 0
Streak: 0
Video: When to use which law! ⚖️
Watch this video to visualize the different triangle cases and when to apply the correct law. 🤓
Practice Problems
Solve the following for the missing side or angle!
1) Given: $a=5$, $b=7$, $C=60^\circ$. Find side $c$. (Round to 2 decimal places)
2) Given: $A=40^\circ$, $B=60^\circ$, $c=10$. Find side $a$. (Round to 2 decimal places)
3) Given: $a=3$, $b=4$, $c=5$. Find angle $C$. (e.g., 90)
4) Which law do you use for SAS? (Sines or Cosines)
⚡ Law of Sines & Cosines Speed Quiz
Time: 0
Correct: 0
Press Start
Download CSV Log
Track all practice & quiz answers in a CSV file.