Vocabulary and Notes Introduction to Chapter 8

Right Angle Triangles and Trigonometry  Right angle triangles have two perpendicular legs that create a right angle.  The other two angles can be of any measure.  However, we are most interested in right angle triangles that have measures of either or for their angles.

Legs of right triangles  Right angle triangles have a hypotenuse, which is across from the right angle, and two other legs.  If the two legs are of different lengths they are referred to as the “long leg” and “short leg” of the triangle.  Otherwise, when they are of equal lengths, they are referred to as simply the “legs” of the triangle. Hypotenuse comes from the Greek words for “under tension”, meaning “stretched”.

Legs of right triangles  The ratios of the legs of the right triangles are important.  The ratios define the relative lengths of each leg. That is, the measure of each leg when compared to the other legs.

Legs of right triangles  This means that if you know the measure of one leg you can find the others by using these known ratios.  Because of this we often express the measure of the legs in terms of “x”.

The Pythagorean Theorem  The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the two legs.  hypotenuse 2 = (shorter leg) 2 + (longer leg) 2  hypotenuse 2 = (leg) 2 + (leg) 2  Often shown as: a 2 + b 2 = c 2 or x 2 + y 2 = z 2

Working with radicals  Because the relationship between the legs and hypotenuse involve terms that are squared we need to take the square root to solve for unknowns.  The square root symbol, √, is also known as the radical.  We sometimes need to simplify the radical expression. This means we reduce the term that involves the radical to one that involves prime factors that cannot be further reduced.  We do this by building factor trees, or a tree of the factors that can be derived from the number.

Working with radicals

Your turn! Self Assessment: when you are done, write down how you would rate yourself on working with radicals from 1 to 4. 1 = I don’t understand; 2 = I kind of get it but still need help; 3 = I can do this with just a little help; 4 = I have this down and can explain it to others.

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