Math 109

Section 5.4

Special Right Triangle

Theorem 5.4.1 (45° – 45° – 90°)

In a triangle whose angles measure 45°, 45°, and 90°, the hypotenuse has a length equal to the product of and the length of either leg.

Theorem 5.4.2 (30° – 60° – 90°)

In a triangle whose angles measure 30°, 60°, and 90°, the hypotenuse has a length equal to twice the shorter leg, and the length of the longer leg is the product of and the length of the shorter leg.

Examples

1) Given BC = 5 and ∆ABC is a 30° – 60° – 90° , find AC and AB

2) Given AB = 12 and ∆ABC is a 30° – 60° – 90° , find AC and BC.

3) Given AB = 14 and ∆ABC is a 45° – 45° – 90° , find AC and BC

4) Given AB = 14 and ∆ABC is a 45° – 45° – 90° , find AC and BC

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The angles are 30° and 60°