107 LearnersLast updated on June 25th, 2025
Law Of Sines Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about the Law of Sines Calculator.
What is the Law of Sines Calculator?
A Law of Sines Calculator is a tool used to solve for unknown sides or angles in a triangle using the law of sines.
This law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle.
The calculator makes solving trigonometric problems much easier and faster, saving time and effort.
How to Use the Law of Sines Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the known values: Input the known side lengths and angles into the given fields.
Step 2: Click on calculate: Click on the calculate button to solve for the unknowns.
Step 3: View the result: The calculator will display the result instantly.
How to Apply the Law of Sines?
To apply the law of sines, use the following formula: (a/sin A) = (b/sin B) = (c/sin C) Where a, b, and c are the sides of the triangle, and A, B, and C are the opposite angles. This formula helps to find unknown sides or angles when given enough information about the triangle.
Tips and Tricks for Using the Law of Sines Calculator
When using a Law of Sines Calculator, there are a few tips and tricks to consider:
Make sure to input the correct values for sides and angles, especially distinguishing between degrees and radians.
Be aware that there might be two possible solutions for certain triangles (ambiguous case).
Use the calculator to cross-check your manual calculations, especially in complex scenarios.
Common Mistakes and How to Avoid Them When Using the Law of Sines Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible for errors to occur when using a calculator.
Mistake 1
Ignoring the Ambiguous Case in Triangle Solutions
In some triangles, two different angle solutions may exist (ambiguous case).
Ensure you check for both possibilities when calculating angles.
Mistake 2
Incorrectly entering angle measurements
Ensure angles are entered in the correct unit (degrees or radians) as required by the problem or calculator settings.
Mistake 3
Misinterpreting the Side-Angle Relationship
Ensure each side corresponds to its opposite angle. Mislabeling can lead to incorrect calculations.
Mistake 4
Overlooking Calculator Assumptions
Remember that some calculators may assume certain conditions or default to specific units, which could affect results. Double-check settings before calculations.
Mistake 5
Relying on an incomplete set of data
Ensure you have enough given information to solve the triangle using the law of sines.
Without sufficient data, calculations cannot proceed accurately.
Law of Sines Calculator Examples
Problem 1
Using the Law of Sines, find the unknown angle in a triangle where side a = 7, side b = 9, and angle A = 30°.
Use the formula: (a/sin A) = (b/sin B) (7/sin 30°) = (9/sin B) sin B = 9 * sin 30° / 7 sin B ≈ 0.6429 B ≈ arcsin(0.6429) ≈ 40.1°
Explanation
By applying the law of sines, we find the sine of angle B and then use the inverse sine function to determine the angle.
Problem 2
A triangle has sides a = 5, c = 8, and angle C = 45°. Calculate angle A using the Law of Sines.
Use the formula: (c/sin C) = (a/sin A) (8/sin 45°) = (5/sin A) sin A = 5 * sin 45° / 8 sin A ≈ 0.4419 A ≈ arcsin(0.4419) ≈ 26.2°
Explanation
Using the given sides and angle, we apply the law of sines to find the sine of angle A, then use the arcsin function to find the angle.
Problem 3
Find side c in a triangle with sides a = 6, angle A = 50°, and angle C = 60°.
Use the formula: (a/sin A) = (c/sin C) (6/sin 50°) = (c/sin 60°) c = 6 * sin 60° / sin 50° c ≈ 6.63
Explanation
Using the law of sines, we solve for side c by cross-multiplying and substituting the known values.
Problem 4
In a triangle, side b = 10, angle B = 40°, and angle C = 70°. Find side c.
Use the formula: (b/sin B) = (c/sin C) (10/sin 40°) = (c/sin 70°) c = 10 * sin 70° / sin 40° c ≈ 14.92
Explanation
The law of sines allows us to solve for side c by applying the given angles and side length.
Problem 5
Calculate angle B in a triangle with sides a = 12, b = 9, and angle A = 35° using the Law of Sines.
Use the formula: (a/sin A) = (b/sin B) (12/sin 35°) = (9/sin B) sin B = 9 * sin 35° / 12 sin B ≈ 0.4293 B ≈ arcsin(0.4293) ≈ 25.4°
Explanation
Applying the law of sines, we find the sine of angle B and use the arcsin function to determine the angle.
FAQs on Using the Law of Sines Calculator
1.How do you calculate angles using the Law of Sines?
2.Can the Law of Sines solve all triangles?
3.Why might there be two solutions using the Law of Sines?
4.How do I enter angles in a Law of Sines calculator?
5.Is the Law of Sines calculator accurate?
Glossary of Terms for the Law of Sines Calculator
- Law of Sines: A formula used to relate the sides and angles of a non-right triangle.
- Ambiguous Case: A situation where two different triangles satisfy the given conditions.
- Sine Function: A trigonometric function relating the angle of a right triangle to the ratio of the opposite side to the hypotenuse.
- Arcsin: The inverse function of sine, used to find an angle when its sine value is known.
- Degrees/Radians: Units of measurement for angles used in trigonometry calculations.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
