30 60-90 triangles

Special Right Triangles

30 – 60 – 90 Triangles

Special Right Triangles Directions

As you view this presentation, take notes and work out the practice problems.

When you get to the practice problem screens, complete the step in your notebook before continuing to the next slide.

30- 60- 90 Triangles

l

s

30o

60o

h

• In a 30 – 60 – 90 triangle, the side across from the 30o angle is the short side and often labeled s.

• In a 30 – 60 – 90 triangle, the side across from the 60o angle is the long side and often labeled l.

• The hypotenuse is often labeled h.

30- 60- 90 TrianglesUnderstanding the Shortcuts

s

30o

60o

hl

To understand the relationship between the short side and the hypotenuse, draw a second 30 - 60 – 90 triangle with the same dimensions as the original triangle. Arrange the triangles to form an equilateral triangle with side l as the common side.

30- 60- 90 TrianglesUnderstanding the Shortcut for Finding the Length

of the Hypotenuse

s

30o

60o

hl

h

s

Because the triangle is an equilateral triangle, s + s = h or 2s = h

30- 60- 90 TrianglesUnderstanding the Shortcut for Finding the Length of

the Long Leg

s

30o

60o

h = 2sl

h

s

The Pythagorean Theorem is used to show the relationship between the long side, l, the short side, s, and the hypotenuse, h.

s2 + l2 = h2

s2 + l2 = (2s)2

l2 = 4s2 – s2

l2 = 3s2

= l = s

30- 60- 90 TrianglesUsing the Shortcuts when s is Known

s

30o

60o

h = 2sl = s

When the Short Side is known:

Short side = s

Long side = s

Hypotenuse = 2s

30- 60- 90 TrianglesPractice Problem 1

s = 5

30o

60o

Finding the lengths of the hypotenuse and long side when

s = 5 l = ? h= ?


s = 5

30o

60o

h = 2sl = s

Finding the lengths of the hypotenuse and long side when

s = 5

Remember the shortcuts


30o

60o

h = 10l = 5

l = s = 5

h = 2s = 2* 5 = 10

Finding the lengths of the hypotenuse and long side

s = 5


s = 5

30- 60- 90 TrianglesUsing the Shortcuts when l is Known

s =

30o

60o

h = l

Long Side = l

Short Side l = sl/ = s / = s

Hypotenuse h = 2sOR

h = 2( ) h =


30o

60o

Finding the lengths of the hypotenuse and short side when

l = 7 l = 7 h = ?

s = ?


30o

60o


l = 7


l = 7

s =

h = 2s = =


30o

60o


l = 7


s = =

h = 2s = 2()=

l = 7

s =

h =

30- 60- 90 TrianglesUsing the Shortcuts when h is Known

s = h/2

30o

60o

h l =

Hypotenuse = h

Short Side h = 2sh/2 = 2s/2h/2 = s

Long Side l = s OR l = (h/2)


30o

60o

Finding the lengths of the short side and the long side when

h = 1h = 1

s = ?

l = ?

s = h/2

30o

60o

h = 1 l =


h = 1



s =

30o

60o

h = 1l =


h = 1


s = =

l = s = ( =


s =

30o

60o

h = 1 l =

In the Unit Circle:

h = 1

So remembering these shortcuts for the 30 – 60 – 90 triangle will save you time and work.

s =

l =

30- 60- 90 Trianglesin the Unit Circle

30 60-90 triangles

Education

Transcript of 30 60-90 triangles