A triangle is a form of a polygon with three sides or edges and vertices. A polygon is a two dimensional, closed, and flat with multiple corners. Sides of a triangle form the basic shape in geometry. Ideally, A, B, and C are used to denote three sides.
The sum of three angles forms the interior angles in this shape which is 180 degree. A line segment that joins a triangle’s vertex to the centre point in opposite sides is called a median. The end in the interaction of medians is called the centroid, while the length in the right angles from vertex is called altitude.
According to Euclidean geometry, a non-collinear having three points’ forms an inimitable plane which has a distinctive plane. It is, therefore, stays in a single plane. However, this statement isn’t applicable in higher-dimensional Euclidean spaces.
In this segment, students will learn ways to use triangle formula sides and their limitations in an equation.
How to Find the Side of a Triangle?
To find the sides in this shape, one can use various methods like Sine and Cosine rule, Pythagoras theorem and a triangle’s angle sum property. Students need to know how to apply these methods, which is based on the parameters and conditions provided.
Ideally, there are three types of this shape based on the length in the sides of a triangle. They are-
Isosceles Triangle
Scalene Triangle
Equilateral Triangle
To find a side of a triangle, we can use Pythagoras theorem. Here is an explanation on how to apply this formula.
How to Find the Third Side of a Triangle Using Pythagoras Theorem?
In a right-angled triangle, if perpendicular and base of hypotenuse are its sides, then this theorem says that the square hypotenuse side will be similar to base square and perpendicular square’s sum.
We can use formula Hypotenuse² = Base² + Perpendicular²
Therefore, by knowing two sides in this shape, one can easily find the third side of the triangle. Even the angle sum property and the total sum interior angles will always be 180 degrees.
What is the Third Side of a Triangle When one Uses Perimeter Formula?
The perimeter of this shape is always equal to the sum of its sides. By using this, we can find the total length. One can consider a triangle with sides B, C, D then according to this theorem the formula will be -
Perimeter will be BCD = BC + BD + CD
If two sides of this shape and its perimeter is given, then finding the length of the third side of triangle will be hassle-free.
If an equation gives only an angle of a side length, then one can use the rule trigonometry ratio to find other sides. In a triangle with θ angle between two sides then the sine, cos and tan ratio will be-
Cos θ = Length of bottom side divided by Length of Hypotenuse side
Sine θ = Length of contrary side divided by Length of Hypotenuse side
Tan θ = Length of a right-angle side divided by Length of Base side
Apart from practising equations based on sides of a triangle, a student needs proper guidance on related theorems. For strengthening base on mathematical equations, they require top-notch study materials and test papers.
One can check Vedantu, which is a trustworthy education site offering solutions on the sum of two sides of a triangle equal to third and more. Apart from test papers, they offer pocket-friendly live classes and CBSE based notes. If you desire to rank flying high grades, don’t forget to download the app today.
FAQs on Sides of a Triangle
1. What are the different types of triangles based on the length of their sides?
Based on the lengths of their sides, triangles are classified into three main types:
- Equilateral Triangle: A triangle where all three sides are of equal length. Consequently, all three angles are also equal (60°).
- Isosceles Triangle: A triangle with two sides of equal length. The angles opposite these two equal sides are also equal.
- Scalene Triangle: A triangle in which all three sides have different lengths. As a result, all three interior angles are also different.
2. What is the main rule that the sides of a triangle must follow?
The primary rule for the sides of any triangle is the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side. For a triangle with side lengths a, b, and c, the following conditions must all be true: a + b > c, a + c > b, and b + c > a.
3. How can you find the length of a missing side in a right-angled triangle?
To find the missing side of a right-angled triangle, you can use the Pythagorean theorem. The theorem states that the square of the hypotenuse (the side opposite the right angle, 'c') is equal to the sum of the squares of the other two sides ('a' and 'b'). The formula is a² + b² = c². If you know the lengths of any two sides, you can rearrange this formula to solve for the unknown side.
4. Can any three lengths be used to form a triangle? Explain why or why not.
No, not just any three lengths can form a triangle. They must satisfy the Triangle Inequality Theorem. For instance, side lengths of 5 cm, 7 cm, and 10 cm can form a triangle because 5+7 > 10. However, side lengths of 3 cm, 4 cm, and 8 cm cannot form a triangle because the sum of the two shorter sides (3 + 4 = 7) is not greater than the longest side (8).
5. How are the lengths of a triangle's sides related to its angles?
There is a direct relationship between the lengths of a triangle's sides and the measure of its opposite angles:
- The longest side is always opposite the largest angle.
- The shortest side is always opposite the smallest angle.
- If two sides are equal (an isosceles triangle), the angles opposite them are also equal.
This principle helps in understanding the geometry of a triangle without needing all measurements.
6. Do the sides of a triangle add up to 180 degrees?
This is a common point of confusion. It is the sum of the three interior angles of a triangle that always equals 180 degrees, not the lengths of its sides. The sum of the side lengths is called the perimeter, and it can vary for every triangle. For example, a triangle can have side lengths 3, 4, 5 or 10, 11, 12; their perimeters are different, but the sum of their angles is always 180°.
7. What is the perimeter of a triangle and how is it calculated?
The perimeter of a triangle is the total distance around its boundary. It is calculated by simply adding the lengths of its three sides. If a triangle has side lengths denoted by a, b, and c, the formula for the perimeter (P) is P = a + b + c. The perimeter is always measured in units of length, such as centimetres (cm) or metres (m).
