Title: Special%20Right%20Triangles
1Lesson 7-3
Special Right Triangles
245-45-90 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
345-45-90 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
430-60-90 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
530-60-90 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
6Example 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
7Example 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