Find side x
Use Law of Sines. Round to 1 decimal place.
Law of Sines Quest!
Solve non-right triangles.
Law of Sines Game
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This Law of Sines Game is a great way to put your skills to the test in a fun environment. By practicing, you’ll start to work out the answers efficiently.
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Law of Sines Game
The Law of Sines is a rule that relates the sides and angles of any triangle (not just right-angled triangles). You use it when you have a known pair of a side and its opposite angle, plus one other piece of information (either another side or another angle). Scroll down the page for a more detailed explanation.
This game focuses on non-right triangles and requires applying the Law of Sines: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\).
If you give a wrong answer, the game will provide the correct answer.
Score: 0 / 0
How to Play the Law of Sines Game
This game focuses on non-right triangles and requires applying the Law of Sines: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\).
Here’s how to play:
- Choose your challenge: Select “Find Missing Side”, “Find Missing Angle”, or “Mixed Challenge”.
- Find Missing Side Given two angles and a side.
- Find Missing Angle Given two sides and an angle.
- Check Your Work: The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
- Get a New Problem: It will then show you a new problem.
Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried. - Back to Menu Click “Menu” to restart the game.
Find Law of Sines
The Law of Sines is a rule that relates the sides and angles of any triangle (not just right-angled triangles). You use it when you have a known pair of a side and its opposite angle, plus one other piece of information (either another side or another angle).
Law of Sines Formula
For any triangle with angles A, B, and C, and the sides opposite those angles labeled a, b, and c, the Law of Sines states:
\(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)
This formula can also be written in its reciprocal form, which is often easier for finding angles:
\(\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\)
When to Use the Law of Sines
You must have at least one complete side-angle pair (a side and its opposite angle) to set up the equation. The Law of Sines is used in the following triangle-solving cases:
- AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle): Two angles and any side.
- SSA (Side-Side-Angle): Two sides and a non-included angle. This is known as the Ambiguous Case because the given information can sometimes result in zero, one, or two possible triangles.
If given SSS (Side-side-Side) or SAS (Side-Angle-Side) then use the Law of Cosines.
The video gives a clear, step-by-step approach to learn how to find angles and sides using the Law of Sines.
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