how to find the third side of a triangle

Triangle Calculator

Please provide 3 values including at least i side to the following half dozen fields, and click the "Calculate" button. When radians are selected as the angle unit, it tin have values such every bit pi/2, pi/4, etc.




Angle Unit:

A triangle is a polygon that has iii vertices. A vertex is a point where two or more curves, lines, or edges meet; in the example of a triangle, the three vertices are joined by three line segments called edges. A triangle is unremarkably referred to by its vertices. Hence, a triangle with vertices a, b, and c is typically denoted every bit Δabc. Furthermore, triangles tend to be described based on the length of their sides, every bit well as their internal angles. For case, a triangle in which all three sides have equal lengths is called an equilateral triangle while a triangle in which ii sides have equal lengths is called isosceles. When none of the sides of a triangle take equal lengths, it is referred to as scalene, as depicted beneath.

Tick marks on the border of a triangle are a common notation that reflects the length of the side, where the aforementioned number of ticks means equal length. Similar notation exists for the internal angles of a triangle, denoted by differing numbers of concentric arcs located at the triangle'due south vertices. As can be seen from the triangles above, the length and internal angles of a triangle are direct related, so it makes sense that an equilateral triangle has three equal internal angles, and iii equal length sides. Note that the triangle provided in the calculator is not shown to scale; while it looks equilateral (and has bending markings that typically would be read every bit equal), it is not necessarily equilateral and is only a representation of a triangle. When actual values are entered, the calculator output will reflect what the shape of the input triangle should await like.

Triangles classified based on their internal angles fall into two categories: right or oblique. A right triangle is a triangle in which one of the angles is 90°, and is denoted by two line segments forming a foursquare at the vertex constituting the right angle. The longest border of a correct triangle, which is the edge opposite the right angle, is called the hypotenuse. Any triangle that is not a right triangle is classified as an oblique triangle and tin can either be birdbrained or acute. In an obtuse triangle, 1 of the angles of the triangle is greater than 90°, while in an acute triangle, all of the angles are less than 90°, as shown below.

Triangle facts, theorems, and laws

Information technology is not possible for a triangle to have more than than one vertex with internal bending greater than or equal to 90°, or it would no longer be a triangle.
The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the 2 interior angles that are not adjacent to information technology. Another manner to calculate the exterior bending of a triangle is to subtract the angle of the vertex of interest from 180°.
The sum of the lengths of any two sides of a triangle is always larger than the length of the third side
Pythagorean theorem: The Pythagorean theorem is a theorem specific to right triangles. For whatever right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. Information technology follows that any triangle in which the sides satisfy this condition is a right triangle. There are also special cases of right triangles, such as the 30° 60° xc, 45° 45° 90°, and 3 4 v right triangles that facilitate calculations. Where a and b are two sides of a triangle, and c is the hypotenuse, the Pythagorean theorem can be written as:
a² + b² = cⁱⁱ
EX: Given a = 3, c = v, find b:
3² + b² = 5ⁱⁱ
9 + b² = 25
b² = 16 => b = four
Law of sines: the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using the law of sines makes it possible to detect unknown angles and sides of a triangle given enough data. Where sides a, b, c, and angles A, B, C are as depicted in the above computer, the law of sines can be written as shown below. Thus, if b, B and C are known, it is possible to find c past relating b/sin(B) and c/sin(C). Note that there exist cases when a triangle meets certain conditions, where two unlike triangle configurations are possible given the same set of information.

Given the lengths of all 3 sides of any triangle, each angle can be calculated using the following equation. Refer to the triangle above, assuming that a, b, and c are known values.

Area of a Triangle

At that place are multiple different equations for calculating the area of a triangle, dependent on what information is known. Probable the nearly ordinarily known equation for calculating the area of a triangle involves its base, b, and top, h. The "base" refers to any side of the triangle where the superlative is represented by the length of the line segment drawn from the vertex reverse the base, to a bespeak on the base that forms a perpendicular.

Given the length of 2 sides and the angle between them, the following formula can be used to decide the surface area of the triangle. Annotation that the variables used are in reference to the triangle shown in the estimator in a higher place. Given a = 9, b = 7, and C = thirty°:

Another method for computing the area of a triangle uses Heron'south formula. Unlike the previous equations, Heron'due south formula does non require an arbitrary selection of a side as a base, or a vertex every bit an origin. However, it does crave that the lengths of the 3 sides are known. Again, in reference to the triangle provided in the calculator, if a = 3, b = 4, and c = 5:

Median, inradius, and circumradius

Median

The median of a triangle is divers as the length of a line segment that extends from a vertex of the triangle to the midpoint of the opposing side. A triangle can have three medians, all of which will intersect at the centroid (the arithmetic hateful position of all the points in the triangle) of the triangle. Refer to the effigy provided beneath for clarification.

The medians of the triangle are represented by the line segments m_a, m_b, and thou_c. The length of each median can be calculated as follows:

Where a, b, and c stand for the length of the side of the triangle as shown in the figure above.

As an case, given that a=ii, b=three, and c=4, the median m_a can be calculated as follows:

Inradius

The inradius is the radius of the largest circle that volition fit within the given polygon, in this case, a triangle. The inradius is perpendicular to each side of the polygon. In a triangle, the inradius can be determined by constructing two angle bisectors to determine the incenter of the triangle. The inradius is the perpendicular distance between the incenter and one of the sides of the triangle. Any side of the triangle can be used as long as the perpendicular distance between the side and the incenter is determined, since the incenter, by definition, is equidistant from each side of the triangle.

For the purposes of this reckoner, the inradius is calculated using the area (Area) and semiperimeter (s) of the triangle along with the following formulas:

where a, b, and c are the sides of the triangle

Circumradius

The circumradius is defined as the radius of a circle that passes through all the vertices of a polygon, in this case, a triangle. The center of this circumvolve, where all the perpendicular bisectors of each side of the triangle meet, is the circumcenter of the triangle, and is the point from which the circumradius is measured. The circumcenter of the triangle does not necessarily accept to be within the triangle. It is worth noting that all triangles have a circumcircle (circle that passes through each vertex), and therefore a circumradius.