Transcript Lesson 7-3 Special Right Triangles Lesson 7-3: Special Right Triangles 45°-45°-90° Special Right Triangle In a triangle 45°-45°-90° , the hypotenuse is 2 times as.

Lesson 7-3
Special Right
Triangles
Lesson 7-3: Special Right
Triangles
1
45°-45°-90° Special Right Triangle
In a triangle 45°-45°-90° , the hypotenuse is 2 times as long as
a leg.
Example:
45°
45°
Leg
X
Hypotenuse
5 2 cm
5 cm
X 2
5 cm
45°
Leg
45°
X

Lesson 7-3: Special Right
Triangles
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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 3 times
as long as the shorter leg.
Example:
Hypotenuse
30°
2X
Longer Leg
X 3
30°
10 cm
5 3 cm
60°
60°
Shorter Leg
Lesson 7-3: Special Right
Triangles
5 cm
3
X
Example: Find the value of a and b.
7 cm
b = 14 cm
60°
30°
b
a = 7 3 cm
2x
x 3
30 °
a
60°
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 3.
Step 5: Solve for a and b
Lesson 7-3: Special Right
Triangles
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Example: Find the value of a and b.
7 cm
b = 7 2 cm
45°
45°
b
2
x 2
x
45 °
a = 7 cm
a
45°
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 2.
Step 5: Solve for a and b
Lesson 7-3: Special Right
Triangles
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