Special RightTriangles

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Presentation transcript:

Special RightTriangles

There are 2 special right triangles The first one we’ll talk about is a 45-45-90 The length of the hypotenuse will always be bigger by √2 BEHOLD… an isosceles triangle x√2 x The length of the sides are congruent… let’s call them x. x

Let’s try … mAC = 12 mCB = ____ mAB = ____ 12 12√2 5√2 12√2 12 5√6 2 5√3 12 2 5 5√3 mAC = ____ mCB = ____ mAB = 5√2 5 5 5√3 5√3 mAC = ____ mCB = ____ mAB = 5√6

Given the leg, multiply it by √2 to find the hypotenuse. “The rules” for a 45-45-90 Given the hypotenuse, divide it by √2 to find the leg.

The 2nd special right triangle is a 30-60-90 Shortness rules! Size matters. The lengths of the sides of this triangle are based on the SHORT SIDE.

The smallest angle is across the shortest side. Fun fact: The smallest angle is across the shortest side. Given any side, find the length of the short side first!! Kapish? 7 7√3 14 mAC= ____ mCB= ____ mAB= ____ 8 mAC= ____ mCB= ____ mAB= ____ 8√3 3 16√3 3 4 2 2√3 mAC= ____ mCB= ____ mAB= ____

Try this… Find the perimeter and area of a 30-60-90 Δ with a hypotenuse of 18 units. (sketch it) What is the length of the short leg? What is the length of the long leg? What is the perimeter? (exact) 27 + 9√3 units What is the area? (exact) 81√3 sq units or 40.5√3 units2 2 18 60° 9 30° 9√3

Assignment 8-2 Practice Day 1 Project Piece Exit Pass