How to Find the Length of the Side of a Triangle

Knowing the length of the sides of a triangle has various applications.

Triangles are two-dimensional shapes that are characterized by three sides. Whether you are a high school student in geometry class or an architect attempting to outline a building, finding the length of triangle sides has its academic or practical applications. Without a ruler, knowing one or two sides can help you solve the unknown measurements of a right triangle using the Pythagorean theorem equation.

Things You'll Need

• Calculator

Instructions

Right Triangles

1. Identify the sides and hypotenuse of the triangle. The sides of the triangle will intersect to form a 90-degree angle. The hypotenuse side is the side opposite the 90-degree angle.

2. Implement the Pythagorean theorem, which is defined by A^2 + B^2 = C^2. "A" and "B" represent the regular sides, while "C" represents the hypotenuse.

3. Calculate the squared values of the regular sides and add the resultant values together. For example, if the regular sides of the triangle are 3 inches and 4 inches, the total value would be 25. (3^2 + 4^2 = 25)

4. Find the value of the hypotenuse by finding the square root of the total value of the squared regular sides. For example, if the total value is 25, the square root of 25 would be 5.

5. Assess the shape of the triangle. If the shape is an isosceles right triangle, the two regular sides will be the same length. If the triangle is an equilateral triangle, all three sides will be the same length.

Irregular Triangles

1. Multiply the two given value sides by each other. Unlike the Pythagorean theorem, do not square each number.

2. Multiply the answer found in Step 1 by 2.

3. Obtain a calculator with basic trigonometry functions and multiply the answer found in Step 3 by the cosine of the angle opposite the side of the triangle you are solving for. The answer will be known as the cosine of A ("cosA").

4. Implement the law of cosines to find the length of the unknown side. Enter the two known sides into the following equation on your calculator: B^2 + C^2 - 2BC(cosA). "B" and "C" are the lengths of the two known sides and the "cosA" is the answer you found in Step 3.

5. Take the square root of the value you found in Step 4. The answer will be the length of the unknown side.

References

• AJ Design: Scalene Triangle Equations Formulas Calculator