1. 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.
Example:
45°
45° cm
Hypotenuse
5 cm
Leg X X
45°
5 cm
45°
Leg X
Special Right Triangles

3. 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 a
60° a
Short Leg
Special Right Triangles

4. 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 X cm
60°
60° X
5 cm
Shorter Leg
Special Right Triangles

5. 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 4: From the pattern, we know that x = 7 , b = 2x, and a = x .
Step 5: Solve for a and b
Special Right Triangles

6. Example: Find the value of a and b.
b = cm
45°
7 cm
45° x b x
45 °
45°
a = 7 cm a x
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
Special Right Triangles