Chapter 9 9.1 9.5 Trigonometry 9.7 Vectors

9.1 Similar Right Triangles ∆ ABC ~ ∆ ADB

∆ ABC ~ ∆ CDB

∆ ADB ~ ∆ CDB a) Similar triangles Geometric Mean = Altitude or legs Pythagorean Triple Any positive integer that satisfies the Pythagorean Theorem. Ex.: 3, 4, 5 If a^2+b^2=c^2 then the ∆ is a right ∆.

If c^2< a^2+b^2 then the ∆ is and acute ∆.

If c^2>a^2+b^2 then the ∆ is an obtuse ∆. 9.4 Special Right Triangles With certain right triangles, there is a way to determine the measurements of their sides without two sides already given and without using Pythagorean theorem. 30-60-90 45-45-90 It is a method of finding the other two angles of a

right triangle based off of the length of the sides. Sine Cosine Tangent Sin A = opposite side/ hypotenuse

Cos A= adjacent side/ hypotenuse

Tan A= opposite side/ adjacent side

To solve a right triangle is to determine the measures of all the angles and sides of the right triangle. 9.6 Solving Right Triangles A Vector is a ray on a graph that has an initial point and a terminal point. Direction The direction is the angle of the Vector.

-To find the direction you have to find the angle that is formed at the initial point of the vector. To do that you have to use Tangent, because the triangle formed is a right triangle and the only lengths of the sides known are the legs. Magnitude Component Form Adding Vectors Equal Vectors Parallel Vectors The Magnitude of a vector is its distance.

To find the magnitude use the distance formula.

You can also use Pythagorean Theorem.

To find the component form of the Vector, the formula is: To add two Vectors find their component forms and add them together. Vectors with the same Magnitude. Vectors with the same Direction. b) Finding and using the geometric mean

of right triangles. If the altitude is drawn to the hypotenuse of a right ∆ then the 2 ∆’s formed are ~ to the original ∆ and to each other. 9.2 Pythagorean Triple 9.3 Determining Types of Triangles For example... Pythagorean Theorem Example problem The Formula for a 45-45-90

∆ will always be: Legs = = Hypotenuse Step 1 Step 2 Step 3 Step 4 Step 5 Final Answer The Formula for a 30-60-90

∆ will always be: Leg across from 30 degrees= X

Leg across from 60 degrees= Xv3

Hypotenuse= 2X Example Problem Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Final Answer Altitude The point of the Geometric mean is to find the lengths of the segments. The length of the altitude is the geometric mean of the lengths of the 2 segments. BD/AD = AD/DC Leg Altitude The Length of the Leg is the Geometric Mean

of the two segments. BC/BA=BA/BD For Example: Step 1 Step 2 Step 3 Final Answer Soh-Cah-Toa Simple Examples Problem examples Step 1 Step 2 Step 3 Final Answer If you do not move Sin to the other

side and make it inverse then you will

get the answer wrong. Step 1 Step 2 Step 3 Final Answer Find Sin A Find Sin A Find X Step 1 Step 2 Step 3 Step 4 Final Answer Step 1: Solve for Z Step 2: Solve for x Step 3: Solve for z Final Answer: Step 1 Step 2 Steps 3-5 Final Answer Steps 1-4 Final Answer Find Angle A Solve for y

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