Exploring Right

Triangles

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?

8

6

4

2

-2

-5

x

We can solve this the old school way… using the Distance Formula.

She starts at the origin and stops at the point (-4, 4).8

6

4

2

-2

-5

x

2 2

2 1 2 1x x y y

2 24 0 4 0

2 24 4

16 16 4 232

Insert a horizontal line to create a right triangle.

Or we can try some fancy stuff…

6

24

2

4

4

How about the Pythagorean Theorem?

2 2 2a b c

216 16 x

2 2 24 4 x

232 x216 2 x

4 2 x

6

24

2

4

4

Not fancy enough?

Did you notice that both legs of the right triangle measure 4?

6

24

2

4

445°

That means 45·45·90 right

triangle!!!

6

24

2

4

4

2x, x, x...4,4,

24,4,4

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°

4sin45 =

xOR

4cos45 =

x

4

4

Solving for x, 4 4

x= OR x= , x 5.6569sin45 cos45

WAIT A MINUTE…That’s not the same answer…

4

4

x 5.6569?

4 2 ?

4 2

And using a calculator...

5.6569

4

4

To recap and review…

4 2 5.65697x

Distance Formula

Pythagorean Theorem

Special Right Triangles

TRIGRatios

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.

OR SOHCAHTOA

, 3, 2x x x

How do I know which to use?…