1. 5.1 Special Right Triangles

2. What you should already know… Right triangles have one 90 o angle The longest side is called the HYPOTENUSE  It is directly across from the 90 o The other sides are called LEGS Hypotenuse LEG

3. Pythagorean Theorem The sides of a right triangle satisfy this theorem: a 2 + b 2 = c 2 LEG Hypotenuse

4. Vocabulary 45-45-90 Triangle:  In a 45-45-90 triangle, the hypotenuse is times as long as each leg.

5. Hints for 45-45-90 Leg to Hypotenuse: MULTIPLY by Hypotenuse to Leg: DIVIDE by LEG Hypotenuse = LEG

6. Example 1: Find the value of x. a)b)

7. Vocabulary 30-60-90 Triangle:  In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

8. How do you know which is the shorter leg and which is the longer leg??? We know that the hypotenuse is directly across from the 90 O angle. The shorter leg is across from the smaller angle (30 o ) The longer leg is across from the larger angle (60 O )

9. 30-60-90 Hypotenuse 30 o 60 o Shorter Leg Longer Leg

10. Hints for 30-60-90 Shorter Leg to Hypotenuse: MULTIPLY by 2 Hypotenuse to Shorter Leg: DIVIDE by 2 Shorter Leg to Longer Leg: MULTIPLY by Longer Leg to Shorter Leg: DIVIDE by You always want to work with the Shorter Leg…it makes it easier!

11. 30-60-90 30 o 60 o Shorter Leg Longer Leg = ShorterHypotenuse = 2Shorter

12. Example 2: Find the values of x and y.

13. You Try: Find the value of each variable. 1)2)

14. Homework P. 153 #1-13all