Unit 3 1 Section 3 Special Right Triangles

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Unit 3. 1 Section 3 Special Right Triangles

Unit 3. 1 Section 3 Special Right Triangles

What you should already o angle n Right triangles have one 90 know… n

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

Pythagorean Theorem n The sides of a right triangle satisfy this theorem: a 2

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

Vocabulary n 45 -45 -90 Triangle: q In a 45 -45 -90 triangle, the

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

Hints for 45 -45 -90 n Leg to Hypotenuse: MULTIPLY by n Hypotenuse to

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

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

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

Vocabulary n 30 -60 -90 Triangle: q In a 30 -60 -90 triangle, the

Vocabulary n 30 -60 -90 Triangle: q 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.

How do you know which is the shorter leg and which is the longer

How do you know which is the shorter leg and which is the longer leg? ? ? n We know that the hypotenuse is directly n n 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)

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

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

Hints for 30 -60 -90 n Shorter Leg to Hypotenuse: MULTIPLY by 2 n

Hints for 30 -60 -90 n Shorter Leg to Hypotenuse: MULTIPLY by 2 n Hypotenuse to Shorter Leg: DIVIDE by 2 n Shorter Leg to Longer Leg: MULTIPLY by n Longer Leg to Shorter Leg: DIVIDE by t to n a w s y er t a r w o l h a You ith the S asier! e w t i k r s o ke w a m it … g e L

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

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

Example 2: n Find the values of x and y.

Example 2: n Find the values of x and y.

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

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