Log In Start studying!

Select your language

Suggested languages for you:
StudySmarter - The all-in-one study app.
4.8 • +11k Ratings
More than 3 Million Downloads
Free
|
|

Law of Sines in Algebra

Law of Sines in Algebra

Using trigonometric rules, it is possible to derive various properties and values of right-angled triangles. Using the various triangle rules, it is possible to still apply trigonometry to find out various properties of non right-angled triangles such as unknown angles, lengths or area of the triangle. In this article, we will discuss one of these triangle rules - law of sines.

The Law of Sines

The law of sines rule can be used to find missing sides or angles in a triangle.

Consider the following triangle with sides a, b and c, and angles, A, B and C.

Triangle sine rule - StudySmarter

Triangle with sides a, b and c, and angles, A, B and C, Nilabhro Datta - StudySmarter Originals

There are 2 versions of the Law of Sines.

For the above triangle, the first version of the Law of Sines states

asin(A)=bsin(C)=csin(C)

This version of the Law of Sines is usually used to find the length of a missing side.

The second version of the Law of Sines states

sin(A)a=sin(B)b=sin(C)c

This version of the Law of Sines is usually used to find a missing angle.

When to use the Law of Sines?

The law of sines can be used to solve triangles when two angles and the length of any side are known, or when the lengths of two sides and an angle opposite one of the two sides are known.

Law of Sines Examples

For the following triangle, find a.

Solution

According to the Law of Sines,

asin(A)=bsin(B)asin(75°)=8sin(30°)a0.966=80.5a = 15.455

For the angle, x.

Solution

According to the Law of Sines,

sin(A)a=sin(B)bsin(x)10=sin(50°)15sin(x)10=0.76615x = 30.71°

Law of sines in algebra - Key takeaways

  • The law of sines rule can be used to find missing sides or angles in a triangle.
  • The first version of the Law of Sines states asin(A)=bsin(C)=csin(C)
  • The second version of the Law of Sines states sin(A)a=sin(B)b=sin(C)c
  • The law of sines can be used to solve triangles when two angles and the length of any side are known, or when the lengths of two sides and an angle opposite one of the two sides are known.

Frequently Asked Questions about Law of Sines in Algebra

The Law of Sines states a/sin(A)=b/sin(B)=c/sin(C), for a triangle with sides a, b and c, and angles, A, B and C.

If two sides and an angle opposite one of the two sides is given, then the law of sines can be used to find the value of the other angle.

The law of sines can be used to solve triangles when two angles and the length of any side are known, or when the lengths of two sides and an angle opposite one of the two sides are known.

Final Law of Sines in Algebra Quiz

Question

A triangle has two sides of length 6 and 7, and the angle opposite the side with length 7 is 72°. Find the angle opposite the side of length 6.

Show answer

Answer

54.6

Show question

Question

What is the sine rule used for?

Show answer

Answer

To find missing sides or angles in a triangle.

Show question

Question

A triangle has side lengths of 10, x and y, with angles of 30°, 85° and 65°. Use the sine rule to find the value of x and y. The side of length 10 is opposite the angle measuring 30°.

Show answer

Answer

19.9 and 16.1 

Show question

More about Law of Sines in Algebra
60%

of the users don't pass the Law of Sines in Algebra quiz! Will you pass the quiz?

Start Quiz

Discover the right content for your subjects

No need to cheat if you have everything you need to succeed! Packed into one app!

Study Plan

Be perfectly prepared on time with an individual plan.

Quizzes

Test your knowledge with gamified quizzes.

Flashcards

Create and find flashcards in record time.

Notes

Create beautiful notes faster than ever before.

Study Sets

Have all your study materials in one place.

Documents

Upload unlimited documents and save them online.

Study Analytics

Identify your study strength and weaknesses.

Weekly Goals

Set individual study goals and earn points reaching them.

Smart Reminders

Stop procrastinating with our study reminders.

Rewards

Earn points, unlock badges and level up while studying.

Magic Marker

Create flashcards in notes completely automatically.

Smart Formatting

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.

Get FREE ACCESS to all of our study material, tailor-made!

Over 10 million students from across the world are already learning smarter.

Get Started for Free
Illustration