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Trig. Day 3

Special Right Triangles

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45°-45°-90° Special Right Triangle

245°

45°

Hypotenuse

XX

X

Leg

Leg

Example:

45°

45°

5 cm

5 cm

5 cm

2

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30°-60°-90° Special Right Triangle

30°

60°

Hypotenuse

3X

2X

X

Longer Leg

Shorter Leg

Example:

30°

60°

10 cm

5 cm

5 cm3

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Example: Find the value of a and b.

60°7 cm

a

b

Step 1: Find the missing angle measure. 30°

30 °

Step 2: Decide which special right triangle applies. 30°-60°-90°

Step 3: Match the 30°-60°-90° pattern with the problem.

30°

60°

x

2x3x

a = cm

b = 14 cm

Step 5: Solve for a and b

7 3

Step 4: From the pattern, we know that x = 7 , b = 2x, and a = x .3

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Example: Find the value of a and b.

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45°7 cm

a

b

Step 1: Find the missing angle measure. 45°

45 °

Step 2: Decide which special right triangle applies. 45°-45°-90°

Step 3: Match the 45°-45°-90° pattern with the problem.

45°

45°

x

xx

Step 4: From the pattern, we know that x = 7 , a = x, and b = x .

a = 7 cm

b = 7 cm

Step 5: Solve for a and b

2

2

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