How to find the missing side of a triangle?

Mathematics
1

how to find the missing side of a triangle

@aibot

2

To find the missing side of a triangle, you can use the Pythagorean theorem or trigonometric ratios. Let’s discuss both methods:

  1. Pythagorean Theorem:
    If you have a right triangle (one angle is 90 degrees), you can use the Pythagorean theorem to find the missing side. The theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, or the hypotenuse.

Here’s how you can use the Pythagorean theorem:

  • Identify the right triangle and label the sides. The longest side is the hypotenuse, typically labeled as ‘c’, and the other two sides are the shorter sides, labeled as ‘a’ and ‘b’.
  • Determine which side is missing and label it as ‘x’.
  • Apply the Pythagorean theorem equation: a² + b² = c².
  • Substitute the known side lengths into the equation and solve for the missing side ‘x’.
  1. Trigonometric Ratios:
    If you have a non-right triangle, you can use trigonometric ratios to find the missing side. The three primary ratios are sine, cosine, and tangent.

Here’s how you can use trigonometric ratios:

  • Identify the triangle and label the sides and angles. The side opposite the given angle is typically labeled as ‘x’, while the hypotenuse is labeled as ‘h’.
  • Determine which side is missing and label it as ‘x’.
  • Use the appropriate trigonometric ratio to solve for the missing side, depending on the given information.

For example, to find a missing side using sine, the equation would be sin(angle) = x/h. To find a missing side using cosine, the equation would be cos(angle) = x/h. And to find a missing side using tangent, the equation would be tan(angle) = x/h.

Remember to use the appropriate trigonometric ratio and known values to solve for the missing side ‘x’.

I hope this helps you understand how to find the missing side of a triangle! Let me know if you have any further questions.