Intro to 30-60-90 triangles | Right triangles and trigonometry | Geometry | Khan Academy

TL;DR

This video explains the properties and relationships of 45-45-90 and 30-60-90 triangles, including how to calculate the length of their sides using the Pythagorean theorem.

Transcript

Sorry for starting the presentation with a cough. I think I still have a little bit of a bug going around. But now I want to continue with the 45-45-90 triangles. So in the last presentation we learned that either side of a 45-45-90 triangle that isn't the hypotenuse is equal to the square route of 2 over 2 times the hypotenuse. Let's do a couple o... Read More

Key Insights

• 🦿 45-45-90 triangles have two equal legs and one right angle. The length of each leg is equal to the square root of 2 divided by 2 times the length of the hypotenuse.
• 🔺 30-60-90 triangles have angles measuring 30, 60, and 90 degrees. The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is the square root of 3 divided by 2 times the length of the hypotenuse.
• 🔺 Flipping a 30-60-90 triangle creates an equilateral triangle, where all angles and sides have the same length.
• 🆘 Memorizing the relationships and formulas for 45-45-90 and 30-60-90 triangles can help solve problems quickly and accurately.
• 🔺 The Pythagorean theorem is a useful tool for finding the lengths of sides in right triangles, including 45-45-90 and 30-60-90 triangles.
• 🔺 Understanding the properties of these triangles is valuable in geometry and can be applied to various problem-solving situations.
• 🫵 The presenter encourages viewers to practice and memorize these concepts for standardized tests, where quick problem-solving is essential.

Questions & Answers

Q: How do you calculate the length of the sides in a 45-45-90 triangle?

To calculate the length of the sides in a 45-45-90 triangle, the formula is x = (sqrt(2)/2) * h, where x is the length of either leg and h is the length of the hypotenuse.

Q: Why is the sum of the angles in a triangle always 180 degrees?

The sum of the angles in a triangle is always 180 degrees because the three angles form a straight line or a straight angle.

Q: How are the sides of a 30-60-90 triangle related?

In a 30-60-90 triangle, the side opposite the 30-degree angle is (1/2) times the length of the hypotenuse, and the side opposite the 60-degree angle is (sqrt(3)/2) times the length of the hypotenuse.

Q: How can the Pythagorean theorem be used to find the lengths of the sides in a 30-60-90 triangle?

The Pythagorean theorem can be used to find the lengths of the sides in a 30-60-90 triangle by setting up an equation where the squared length of one side plus the squared length of another side equals the squared length of the hypotenuse.

Summary & Key Takeaways

• The video begins with an explanation of the properties of a 45-45-90 triangle and how to calculate the length of its sides.

• The presenter then introduces a 30-60-90 triangle and explains how its angles and sides are related, using the Pythagorean theorem to find their lengths.

• The video concludes by highlighting the importance of memorizing these relationships for quick problem-solving in standardized tests.