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5.1 Special Right Triangles

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What you should already know… Right triangles have one 90 o angle The longest side is called the HYPOTENUSE It is directly across from the 90 o The other sides are called LEGS Hypotenuse LEG

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Pythagorean Theorem The sides of a right triangle satisfy this theorem: a 2 + b 2 = c 2 LEG Hypotenuse

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Vocabulary 45-45-90 Triangle: In a 45-45-90 triangle, the hypotenuse is times as long as each leg.

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Hints for 45-45-90 Leg to Hypotenuse: MULTIPLY by Hypotenuse to Leg: DIVIDE by LEG Hypotenuse = LEG

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Example 1: Find the value of x. a)b)

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Vocabulary 30-60-90 Triangle: In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

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How do you know which is the shorter leg and which is the longer leg??? We know that the hypotenuse is directly across from the 90 O angle. The shorter leg is across from the smaller angle (30 o ) The longer leg is across from the larger angle (60 O )

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30-60-90 Hypotenuse 30 o 60 o Shorter Leg Longer Leg

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Hints for 30-60-90 Shorter Leg to Hypotenuse: MULTIPLY by 2 Hypotenuse to Shorter Leg: DIVIDE by 2 Shorter Leg to Longer Leg: MULTIPLY by Longer Leg to Shorter Leg: DIVIDE by You always want to work with the Shorter Leg…it makes it easier!

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30-60-90 30 o 60 o Shorter Leg Longer Leg = ShorterHypotenuse = 2Shorter

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Example 2: Find the values of x and y.

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You Try: Find the value of each variable. 1)2)

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Homework P. 153 #1-13all

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