SPECIAL RIGHT TRIANGLES But first a short video

SPECIAL RIGHT TRIANGLES:

But first, a short video introduction on TRIANGLES:

REMEMBER THESE FACTS: Angles are on the INSIDE of a Triangle. Sides are the LINES of a Triangle. Angles are written in degrees (90◦, 30◦, 45◦) All the angles in ANY Triangle always add up to 180◦

RIGHT TRIANGLE & SPECIAL RIGHT TRIANGLES: 45º 60º 30º

WHY SPECIAL RIGHT TRIANGLES: We use these 2 Special Right Triangles when we need to find the LENGTH of an unknown side of a RIGHT TRIANGLE. We use The PYTHAGOREAN THEOREM formula when you know TWO side lengths of a RIGHT TRIANGLE. We use the SPECIAL RIGHT TRIANGLE formulas when we know ONE side of either type of SPECIAL RIGHT TRIANGLE.

Pythagorean Theorem: We use it when we know the length of 2 SIDES of a Right Triangle and we need to find the length of the unknown side. a² + b² = c² c a b

Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 10 in 14 in a² + b² = c²

Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 12 in 18 in a² + b² = c²

Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 25 in 36 in a² + b² = c²

Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 14. 5 in 18. 5 in a² + b² = c²

Example of when to use the Pythagorean Theorem: What is the length of the missing side? 25 in 10 in ? a² + b² = c²

Example of when to use the Pythagorean Theorem: What is the length of the missing side? 64 in ? 18 in a² + b² = c²

What is the difference between these two triangles? : 45º You know EXACTLY what the angles are on the triangle on the LEFT. You DON’T KNOW EXACTLY what the angles are on the triangle on the RIGHT.

Opposite Operations: X + - Opposite X Opposite C² Opposite + c²

45 45 90 Special Right Triangle:

30 60 90 Special Right Triangle:

Practice Problem#1: 45º x√ 2 x 45º x

Practice Problem#1: 60º 2 y y 30º y√ 3

Practice Problem #1 What is the length of the missing side? a² + b² = c²

Practice Problem #1 What is the length of the missing side? ? 10 in 14 in a² + b² = c²

Pythagorean Theorem OR Special Right Triangles? 45º ? 4 in ? 4 in 45º 8 in a² + b² = c² ? Special Right Triangles

Practice Problem #1 What is the length of the missing side? a² + b² = c² OR Special Right Triangles?

MCAS PROBLEM EXAMPLE: T X 6 in 45º W 4 in Y V

MCAS PROBLEM EXAMPLE: T X 6 in 45º W 4 in Y V

MCAS PROBLEM EXAMPLE: X T 6 in 45º W 4 in Y V

T MCAS PROBLEM EXAMPLE: 6 in X 45º V W 4 in Y

When you know the WHOLE and you know a PART, how do you find out what the UNKNOWN PART is? WHOLE - PART UNKNOWN PART