30-60-90 Triangles II | Summary and Q&A

TL;DR

In a 30, 60, 90 triangle, the side opposite the 30-degree angle is half the hypotenuse, while the side opposite the 60-degree angle is equal to the square root of 3 over 2 times the hypotenuse.

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.

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

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.