1. Exploring Right Triangles

2. Dora leaves for a long hike. She walks 6 miles north. Then, she hikes 4 miles west. She then turns and goes 2 miles due south. How far is she from her place of origin?

3. We can solve this the old school way… using the Distance Formula. She starts at the origin and stops at the point (-4, 4).

4. Insert a horizontal line to create a right triangle. Or we can try some fancy stuff …

5. 6 2 4 2 4 4 How about the Pythagorean Theorem?

6. 6 2 4 2 4 4 Not fancy enough? Did you notice that both legs of the right triangle measure 4?

7. 6 2 4 2 4 4 45° That means 45·45·90 right triangle!!!

8. 6 2 4 2 4 4

9. Or we can try some SUPER, SUPER fancy stuff… TRIG!!! This triangle is isosceles with legs equal to 4 Base angles are equal to 45° 4 4 Solving for x,

10. WAIT A MINUTE… That’s not the same answer… 4 4

11. 4 4 To recap and review…

12. Distance Formula Pythagorean Theorem Special Right Triangles TRIG Ratios When you know the coordinates of the endpoints of the segment. When you have the lengths of two sides. When it fits one of the two patterns: 45*45*90 or 30*60*90. When you know the angle measure and at least one other side measure. SOHCAHTOA How do I know which to use?…