How to Find the Long Leg of a 30-60-90 Triangle: Step-by-Step Formula

Learn how to calculate the long leg of a 30-60-90 triangle using the formula long leg = short leg × √3 with easy examples.

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To find the long leg of a 30-60-90 triangle, use the formula: long leg = short leg × √3. The short leg is opposite the 30-degree angle. For instance, if the short leg is 5 units, then the long leg is 5 × √3 ≈ 8.66 units.

FAQs & Answers

  1. What is a 30-60-90 triangle? A 30-60-90 triangle is a special type of right triangle with angles measuring 30°, 60°, and 90°, featuring side lengths in a consistent ratio.
  2. How do you calculate the long leg if you know the short leg? Multiply the length of the short leg by the square root of 3 (√3) to find the long leg.
  3. What is the ratio of the sides in a 30-60-90 triangle? The sides are in the ratio 1 : √3 : 2, corresponding to the short leg, long leg, and hypotenuse respectively.

Watch More

For more in-depth tutorials on special right triangles, check out our videos on how to find the short leg and hypotenuse of 30-60-90 triangles, as well as applications of these formulas in real-world problems.

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