Special Right Triangles - 45 45 90 - Trigonometry & Geometry | SAT Math

TL;DR

Learn how to use the 45-45-90 triangle to solve similar triangles and apply it to SAT or ACT exam questions.

Transcript

in this video we're going to focus on the 45-45-90 triangle now it's important that you understand how to use this triangle so that it can help you solve other triangles or other similar triangles this technique especially useful if you're studying for the sat or the ht exam so let me give you the 45 45 90 reference triangle the first thing you nee... Read More

Key Insights

• 🔺 The 45-45-90 triangle has specific ratios between its sides and is useful in solving similar triangles and exam questions.
• 🙃 The square root of 2 plays a significant role in finding missing sides of the triangle.
• 👻 Understanding the relationships within the 45-45-90 triangle allows for quicker mental calculations and time-saving during exams.

Questions & Answers

Q: What is the 45-45-90 reference triangle and its special properties?

The 45-45-90 triangle is a right triangle with two sides that are equal and the third side is the length of one side multiplied by the square root of two. These properties help in solving similar triangles and SAT/ACT exam questions.

Q: How can you find the missing side of a 45-45-90 triangle given one side length?

If the given side is across the 45 degree angle, you multiply it by the square root of 2. If the given side is across the 90 degree angle, you divide it by the square root of 2.

Q: Can you provide an example of finding the missing sides using the 45-45-90 triangle?

For example, if both legs of the triangle are 8 units long, the hypotenuse would be 8 times the square root of 2. If one leg is 5 times the square root of 2, the other leg would also be 5 times the square root of 2.

Q: How do you find the area of a triangle using the 45-45-90 triangle?

To find the area of a triangle, use the formula: one half base times height. In a 45-45-90 triangle, the base and height are the same, so the formula becomes: one half (side length) squared.

Summary & Key Takeaways

• The 45-45-90 triangle is a right triangle with two sides that are equal and the third side is the length of one side multiplied by the square root of two.

• To find the side across the 90 degree angle, multiply the given side by the square root of 2. To find the side across the 45 degree angle, divide the given side by the square root of 2.

• Practice problems are provided to apply the concept and demonstrate how to use the 45-45-90 triangle to find missing sides.