How to Calculate Side Lengths in a 30-60-90 Triangle

TL;DR

In a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, while the side opposite the 60-degree angle is equal to the hypotenuse multiplied by √3/2. This specific ratio allows you to easily calculate any side length if you know the length of the hypotenuse.

Transcript

Let's continue with the 30, 60, 90 triangles. So just review what we just learned, or hopefully learned-- at minimum what we just saw, --is if we have a 30, 60, 90 -- and once again, remember: this is only applies to 30, 60, 90 triangles --and if I were to say the hypotenuse is of length h, we learned that the side opposite the 30-degree angle, and... Read More

Key Insights

• 🔺 The ratios in a 30, 60, 90 triangle allow for the calculation of side lengths based on the hypotenuse and angle measure.
• 🍰 The side lengths in a 30, 60, 90 triangle have specific relationships, with the shorter side being half the hypotenuse and the longer side being sqrt(3)/2 times the hypotenuse.
• 🔺 The side opposite the 30-degree angle is the shortest side, while the side opposite the 60-degree angle is longer.

Questions & Answers

Q: What are the ratios of sides in a 30, 60, 90 triangle?

In a 30, 60, 90 triangle, the side opposite the 30-degree angle is half the hypotenuse, and the side opposite the 60-degree angle is sqrt(3)/2 times the hypotenuse.

Q: How can the length of a specific side be calculated?

If the hypotenuse and the angle measure are known, the length of a specific side can be calculated using the ratios mentioned earlier.

Q: How is the side opposite the 30-degree angle different from the side opposite the 60-degree angle?

The side opposite the 30-degree angle is the shortest side and is equal to half the hypotenuse, while the side opposite the 60-degree angle is longer and equal to sqrt(3)/2 times the hypotenuse.

Q: What is the relationship between the longer non-hypotenuse side and the shorter side?

The longer non-hypotenuse side is sqrt(3) times longer than the shorter side in a 30, 60, 90 triangle.

Summary & Key Takeaways

• A 30, 60, 90 triangle has specific ratios for its sides: the side opposite the 30-degree angle is half the hypotenuse, and the side opposite the 60-degree angle is sqrt(3)/2 times the hypotenuse.

• Applying these ratios, the length of a specific side can be calculated if the hypotenuse and the angle measure are known.

• The longer non-hypotenuse side is sqrt(3) times longer than the shorter side.