4.8 • +11k Ratings
Save
Print
Edit
It is possible to derive various properties and values of right-angled triangles using trigonometric rules. But what if we are dealing with triangles that don't have any right angles? Can we still apply trigonometry to find out various properties of the given triangles, such as unknown angles, lengths, or area?
The triangle rules discussed in this article will explore this question in further detail:
The first triangle rule that we will discuss is called the sine rule. The sine 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 with sides a, b and c, and angles, A, B and C, Nilabhro Datta - StudySmarter Originals
There are two versions of the sine rule.
For the above triangle, the first version of the sine rule states:
This version of the sine rule is usually used to find the length of a missing side.
The second version of the sine rule states:
This version of the sine rule is usually used to find a missing angle.
For the following triangle, find a.
According to the sine rule,
Read Sine and Cosine Rules to learn about the sine rule in greater depth.
For this triangle, find x.
According to the sine rule,
The second triangle rule that we will discuss is called the cosine rule. The cosine 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.
There are two versions of the cosine rule.
For the above triangle, the first version of the cosine rule states:
a² = b² + c² - 2bc · cos (A)
This version of the cosine rule is usually used to find the length of a missing side when you know the lengths of the other two sides and the angle between them.
The second version of the cosine rule states:
This version of the cosine rule is usually used to find an angle when the lengths of all three sides are known.
Find x.
According to the cosine rule,
a² = b² + c² - 2bc · cos (A)
=> x² = 5² + 8² - 2 x 5 x 8 x cos (30)
=> x² = 19.72
=> x = 4.44
For the next triangle, find angle A.
According to the cosine rule,
Read Sine and Cosine Rules to learn about the cosine rule in greater depth.
We are already familiar with the following formula:
But what if we do not know the exact height of the triangle? We can also find out the area of a triangle for which we know the length of any two sides and the angle between them.
Consider the following triangle:
The area of the above triangle can be found by using the formula:
Find the area of the triangle.
Click on Area of Triangles to learn about the area of triangles rule in greater depth.
The second version of the sine rule states that
The sine rule for triangles states that
a/sin(A)=b/sin(B)=c/sin(C)
The sine rule can be used to find find missing sides or angles in a triangle. Once we have sufficient information, we can used the formula Area=1/2*a*b*sin(C)
Yes, in that case, one of the angles will be 90.
Be perfectly prepared on time with an individual plan.
Test your knowledge with gamified quizzes.
Create and find flashcards in record time.
Create beautiful notes faster than ever before.
Have all your study materials in one place.
Upload unlimited documents and save them online.
Identify your study strength and weaknesses.
Set individual study goals and earn points reaching them.
Stop procrastinating with our study reminders.
Earn points, unlock badges and level up while studying.
Create flashcards in notes completely automatically.
Create the most beautiful study materials using our templates.
Sign up to highlight and take notes. It’s 100% free.
