Special Right Triangles
Vocabulary

45-45-90 Triangle:

In a 45-45-90 triangle, the hypotenuse is
times as long as each leg.
2
Hints for 45-45-90

Leg to Hypotenuse: MULTIPLY by

Hypotenuse to Leg: DIVIDE by
LEG
2
2
Hypotenuse = LEG
LEG
2
Example 1:

a)
Find the value of x.
b)
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 3 times as
long as the shorter leg.
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 90O angle.
The shorter leg is across from the smaller
angle (30o)
The longer leg is across from the larger angle
(60O)
30-60-90
30o
Longer Leg
Hypotenuse
60o
Shorter Leg
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
3
3
30-60-90
30o
Longer Leg = Shorter 3
Hypotenuse = 2Shorter
60o
Shorter Leg
Example 2:

Find the values of x and y.
Find the value of each variable.
1)
2)
