What is how to find the missing side of a triangle?

Here's information on how to find the missing side of a triangle:

Finding a Missing Side of a Triangle

The method you use to find a missing side of a triangle depends on what information you already have. Here are the common scenarios and applicable techniques:

• Right Triangles: If you know the triangle is a right%20triangle (contains a 90-degree angle), you can use:

  • The Pythagorean Theorem: This theorem states that in a right triangle, a² + b² = c², where a and b are the lengths of the legs (the sides adjacent to the right angle), and c is the length of the hypotenuse (the side opposite the right angle). If you know the lengths of two sides, you can solve for the third.

  • Trigonometric Ratios (SOH CAH TOA): If you know one of the acute angles (angles less than 90 degrees) and the length of one side, you can use trigonometric ratios like sine (sin), cosine (cos), or tangent (tan) to find the missing side. SOH CAH TOA is a mnemonic:

    • SOH: Sin(angle) = Opposite / Hypotenuse
    • CAH: Cos(angle) = Adjacent / Hypotenuse
    • TOA: Tan(angle) = Opposite / Adjacent

• Non-Right Triangles (Oblique Triangles): If the triangle does not have a right angle, you'll need to use:

  • Law of Sines: This law states that a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the side lengths, and A, B, and C are the angles opposite those sides, respectively. You can use the Law of Sines if you know:

    • Two angles and one side (AAS or ASA)
    • Two sides and an angle opposite one of them (SSA) - be careful, this case can have ambiguous solutions!

  • Law of Cosines: This law is useful when you know:

    • Three sides (SSS)
    • Two sides and the included angle (SAS) - the angle between the two known sides.

    The Law of Cosines has three forms:

    • a² = b² + c² - 2bc * cos(A)
    • b² = a² + c² - 2ac * cos(B)
    • c² = a² + b² - 2ab * cos(C)