How to Calculate Missing Side of a 30-60-90 Triangle

Learn how to find the missing side of a 30-60-90 triangle using simple ratios.

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To find the missing side of a 30-60-90 triangle, use these properties: the ratio of the sides is 1:√3:2. If the side opposite the 30° angle (the shortest side) is known, multiply it by √3 to find the side opposite the 60° angle, and by 2 for the hypotenuse. For example, if the shortest side is 5, then the hypotenuse is 10 and the other side is 5√3.

FAQs & Answers

  1. What are the side ratios in a 30-60-90 triangle? The side ratios in a 30-60-90 triangle are 1:√3:2.
  2. How do you derive the formula for the side lengths? The lengths can be derived from the properties of right triangles and trigonometric ratios.
  3. Can I use this method for other types of triangles? This specific method applies to 30-60-90 triangles; other triangles require different approaches.

Watch More

For more insights on triangle calculations, check out our videos on other triangle types, like isosceles and equilateral triangles.

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  3. 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.
  4. How to Identify a 30-60-90 Triangle: Essential Tips Learn how to identify a 30-60-90 triangle using angle measurements and side length ratios.
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  7. How to Find Side Lengths of a 45-45-90 Triangle: Step-by-Step Guide Learn how to calculate the side lengths of a 45-45-90 triangle using the special properties of this right triangle.
  8. Calculating the Hypotenuse of a 45-45-90 Triangle: A Step-by-Step Guide Learn how to easily find the hypotenuse of a 45-45-90 triangle with our quick and clear guide.
  9. Understanding the 45-45-90 Triangle Formula Discover the formula for a 45-45-90 triangle and learn how to calculate its sides effectively.
  10. How to Calculate the Missing Side of an Isosceles Triangle Using the Pythagorean Theorem Learn how to find the missing side of an isosceles triangle with our step-by-step guide using the Pythagorean theorem.
  11. Understanding the 3 4 5 Rule: A Simple Check for Right Triangles Learn about the 3 4 5 rule for right triangles and its practical applications in construction and carpentry.
  12. Understanding the 3-4-5 Rule in Right Triangles Learn how the 3-4-5 rule helps you quickly identify right angles in triangles.