Sides Of a Triangle

The sides of a triangle are straight lines that are connected together by the triangle’s three vertices, which are also straight lines. Or, to put it another way, we can say that the sides of a triangle are line segments that come together at the triangular vertices of the triangle. Finding the sides of a right-angled triangle can be accomplished using a variety of approaches, such as the Pythagorean theorem or the triangle’s circumference (or perimeter). If we know the angles and lengths of some of the sides of a triangle, we may apply the law of cosines or the law of sines to determine the lengths of the remaining sides of the triangle.

Sides of Triangle Formula

The trigonometric ratios are related to the sides of a triangle formula, which can be used to compute the sides of a given triangle. The necessary requirements are one side of the triangle and an acute angle, and we can use this information to figure out the rest of the triangle’s sides.

It is possible to apply the Pythagorean theorem straight to a right triangle in this situation.

For an isosceles triangle, we can use either the area or perimeter formulas to find its area or perimeter.

In the case of a general, if we know some of the angles and some of the side lengths, we can apply the law of cosines or the law of sines to solve the problem.

Sides of A Triangle Formula

1. If we are given an angle and a side length for a right triangle, we must find the area of the triangle.

• Sine θ= opposing side length/hypotenuse side length

• Cos θ= neighbouring side length / Hypotenuse side length

• Tan  θ = opposite side/adjacent side length

2. The sine law, which states that sin(A)/a = sin(B)/b = sin(C)/c.

Where, 

• All three sides of the opposing triangles area, b, and c .

• Angles A, B, and C.

3. The law of cosines is defined as c2 = a2 + b2 – 2ab cos (C)

Where,

• The sides of the triangles are represented by the letters a, b, and c.

• The angle formed by the sides a and b is denoted by the letter C.

• We may use the methods above to determine the length of the sides of a triangle based on the values of the triangle that are already known to us.

Sides of Triangle Properties

We have now examined the formulas for determining the lengths of the sides of a triangle; now, let us go over some of the most essential properties of the triangle’s sides:

• This is the longest side of the triangle, as measured from the point where the largest angle of the triangle is formed.

• When the lengths of the corresponding sides of two triangles are equal, two triangles are said to be congruent.

• When the lengths of the respective sides of two triangles are proportional, two triangles are said to be comparable.

• The perimeter of a triangle is defined as the sum of the three sides of the triangle.

• The area of a triangle may be determined using the three sides of a triangle (Heron’s formula), which is represented by the following formula:

• In the equation, area = √[s(s – a)(s – b)(s – c)], the three sides of a triangle (a, b, c) are represented by s, and the semi-perimeter is represented by s.

Sides of Triangle Rule

We have covered the crucial qualities of the triangle’s sides up to this point; now let us look at the triangle’s fundamental rule. Triangles are defined by the rule of three sides, according to which, no matter what lengths any two sides of a triangle are, they are always longer than the length of the third side. This rule is sometimes referred to as the triangle inequality theorem in some circles. As a result, we cannot have a triangle with the lengths 3, 4, and 9 because 3 + 4 = 7 <9 is not possible. 

Important Notes on Sides of Triangle

• The sides of a triangle are straight lines that are connected together by the triangle’s three vertices, which are also straight lines.

• For a right triangle, we can use either the Pythagorean theorem or the trigonometric ratios formula to determine the length of each of its sides.

• When determining the lengths of the sides of a triangle, we can apply either the law of cosines or the law of sines.

Conclusion

In an equilateral triangle, all of the angles are equal. If any of the three line segments is longer than the sum of the other two, it is impossible to form a triangle from those three segments. The triangle inequality theorem asserts that any side of a triangle is always shorter than the sum of the lengths of the other two sides of the triangle. Congruence is the property of two segments in geometry where they have the same length or measurement. In other words, the length of congruent sides of a triangle is the same as its width.  A triangle is a three-sided polygon that has three edges and three vertices, and it has three sides. The most significant attribute of a triangle is that the total of its internal angles is equal to 180 degrees, which is the most common value. The angle sum property of a triangle is the name given to this characteristic.