Find the missing side of a triangle calculator

Finding the missing side or angle couldn't be easier than with our great tool — right triangle side and angle calculator. Choose two given values, type them into the calculator, and the calculator will determine the remaining unknowns in a blink of an eye!

Use our triangle calculator to solve the angles and sides of a triangle using trigonometry. Enter three known values including at least one side to calculate the remaining properties of a triangle. Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications. Full bio.

Find the missing side of a triangle calculator

Please provide 3 values including at least one side to the following 6 fields, and click the "Calculate" button. A triangle is a polygon that has three vertices. A vertex is a point where two or more curves, lines, or edges meet; in the case of a triangle, the three vertices are joined by three line segments called edges. A triangle is usually referred to by its vertices. Furthermore, triangles tend to be described based on the length of their sides, as well as their internal angles. For example, a triangle in which all three sides have equal lengths is called an equilateral triangle while a triangle in which two sides have equal lengths is called isosceles. When none of the sides of a triangle have equal lengths, it is referred to as scalene, as depicted below. Tick marks on the edge of a triangle are a common notation that reflects the length of the side, where the same 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's vertices. As can be seen from the triangles above, the length and internal angles of a triangle are directly related, so it makes sense that an equilateral triangle has three equal internal angles, and three equal length sides. Note that the triangle provided in the calculator is not shown to scale; while it looks equilateral and has angle markings that typically would be read as equal , it is not necessarily equilateral and is simply a representation of a triangle.

If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation. Example Let's show how to find the sides of a right triangle with this tool: Assume we want to find the missing side given area and one side.

Please provide 2 values below to calculate the other values of a right triangle. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry. The sides of a right triangle are commonly referred to with the variables a, b, and c, where c is the hypotenuse and a and b are the lengths of the shorter sides. The altitude divides the original triangle into two smaller, similar triangles that are also similar to the original triangle. If all three sides of a right triangle have lengths that are integers, it is known as a Pythagorean triangle.

Omni's triangle side calculator allows you to calculate the length of the sides of a triangle. There are several methods to find the missing side of a triangle. Depending upon the type of given information, you can choose one of the following:. If we know, the measurements of the two sides and the opposite angle to one of them , we can use the Law of Sines to find the missing side. On the other hand, if we know two sides and the angle between them , we can use the Law of Cosines to find the remaining side. Hence if we know the measurement of the two angles, we can find the third angle using the equation:. Once we know the third angle, we can easily calculate the missing side using the Law of Sines mentioned above.

Find the missing side of a triangle calculator

Finding the missing side or angle couldn't be easier than with our great tool — right triangle side and angle calculator. Choose two given values, type them into the calculator, and the calculator will determine the remaining unknowns in a blink of an eye! If you are wondering how to find the missing side of a right triangle, keep scrolling, and you'll find the formulas behind our calculator. There are a few methods of obtaining right triangle side lengths. Depending on what is given, you can use different relationships or laws to find the missing side:. If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:. If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:. As we remember from basic triangle area formula , we can calculate the area by multiplying the triangle height and base and dividing the result by two. A right triangle is a special case of a scalene triangle, in which one leg is the height when the second leg is the base, so the equation gets simplified to:. For example, if we know only the right triangle area and the length of the leg a , we can derive the equation for the other sides:.

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The law of cosines is a generalization of the Pythagorean theorem that can be used to determine the length of any side of a triangle if the lengths and angles of the other two sides of the triangle are known. This is known as the Pythagorean equation, named after the ancient Greek thinker Pythagoras. If a right triangle is isosceles i. Likely the most commonly known equation for calculating the area of a triangle involves its base, b , and height, h. To find the angles of a right triangle we use trigonometry. Pick the option you need. Be sure that the calculator is set for angle mode rather than radian mode. For a right triangle with sides a and b , and a hypotenuse c , the Pythagorean theorem states:. On the other hand, if we know two sides and the angle between them , we can use the Law of Cosines to find the remaining side. However, if only two sides of a triangle are given, finding the angles of a right triangle requires applying some basic trigonometric functions:. By substituting the known values into the Law of Cosines expression and rearranging, you can solve for side a.

Please provide 2 values below to calculate the other values of a right triangle. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry.

By substituting the known values into the Law of Cosines expression and rearranging, you can solve for any remaining side in a triangle. Side a :. By Joe Sexton. Bike Everyone knows biking is fantastic, but only this Car vs. Purnima Singh , PhD. Enter three known values including at least one side to calculate the remaining properties of a triangle. There are numerous other proofs ranging from algebraic and geometric proofs to proofs using differentials, but the above are two of the simplest versions. The length of each side is 10 cm. The inradius is the perpendicular distance between the incenter and one of the sides of the triangle. The height of a triangle h is equal to 2 times the area A divided by the length of base b. As we know that the perimeter of a triangle is just the sum of its three sides , i. If two sides and the perimeter are known This is the most simple scenario. In the figure above, there are two orientations of copies of right triangles used to form a smaller and larger square, labeled i and ii, that depict two algebraic proofs of the Pythagorean theorem.