Special%20Right%20Triangles

1
Lesson 7-3
Special Right Triangles
2
45-45-90 Special Right Triangle

• In a triangle 45-45-90 , the hypotenuse is
  times as long as a leg.

45
Hypotenuse
Leg
a
a
45
Leg
a
3
45-45-90 Special Right Triangle

• In a triangle 45-45-90 , the hypotenuse is
  times as long as a leg.

Example
45
45
5 cm
Hypotenuse
5 cm
Leg
X
X
45
5 cm
45
X
Leg
4
30-60-90 Special Right Triangle

• In a 30-60-90 triangle, the hypotenuse is
  twice as long as the short leg, and the long leg
  is times as long as the shorter leg.

30
Hypotenuse
2a
Long Leg
60
a
Short Leg
5
30-60-90 Special Right Triangle

• In a triangle 30-60-90 , the hypotenuse is
  twice as long as the shorter leg, and the longer
  leg is times as long as the shorter leg.

Example
Hypotenuse
30
2X
Longer Leg
30
10 cm
60
60
X
Shorter Leg
5 cm
6
Example Find the value of a and b.
b 14 cm
60
7 cm
30
2x
b
30
60
a cm
a
x
Step 1 Find the missing angle measure.
30
Step 2 Decide which special right triangle
applies.
30-60-90
Step 3 Match the 30-60-90 pattern with the
problem.
Step 5 Solve for a and b
7
Example Find the value of a and b.
b 7 cm
45
7 cm
45
x
b
x
45
45
a
x
a 7 cm
Step 1 Find the missing angle measure.
45
Step 2 Decide which special right triangle
applies.
45-45-90
Step 3 Match the 45-45-90 pattern with the
problem.
Step 4 From the pattern, we know that x 7 , a
x, and b x .
Step 5 Solve for a and b