7-2 Right Triangle Trigonometry Pull out those calculators!!!

Absolutes 1.Make sure the calculator is in degrees Scientific: Press DRG button till you see DEG on the face Graphing: Mode then toggle down and toggle left/right to degrees 2.Make sure you know how to find sin/cos/tan of angles Scientific: put in number, then press function Graphing: Function, number, enter

Absolutes 3.If you have a sine or cosine value and want to find the angle, you will use sin -1 or cos -1. These are the inverse functions. Remember the definition of inverse: Put in the answer, get out the original (angle)

Everything will be based on the triangle shown below. As it is called “Right Triangle Trig” you can assume there is a right angle. We will always have the right angle in the same place. A B C a b c Note: B = 42 means angle B = 42.

Examples ΔABC is a right triangle with C = 90 . Solve for the indicated part(s). 1.A = 42 , b = 4; c = ? 2. b = 4, c = 7; B = ?

Word Problems Before we do this, you need to understand 2 standard phrases: Angle of Elevation: ________________ ________________________________ Angle of Depression: _______________ _________________________________

Examples 3.How tall is a tree whose shadow is 47 feet long when the angle of elevation is 49.3 

4. One of the equal sides of an isosceles triangle is 23 cm and the vertex angle is 43 . How long is the base?

8-1 Law of Cosines The first of 2 laws specifically for non-right triangles

Notice: Non-right Triangles We will be using this law when the information given fits: _________________________________

A B C a b c

Area Formula A B C a b c x y

Heron’s Formula Used to find areas of triangles when all sides are given (SSS)

Example Find the area of the triangle A C B

Example Heron’s 1.Given ΔABC with a = 3, b = 4 and c = 5, find the area using Heron’s Formula.

Example 1. a=12; b=5; c=13 Find A

8-2 Law of Sines The second of 2 laws specifically for non-right triangles

Again: Non-right Triangles We will be using this law when the information given fits AAS or ASA patterns.

A B C a b c Law of Sines

Examples 1.Solve ΔABC if a = 5, B= 75º and C = 41º. A=64º

Tom and Steve are 950 ft apart on the same side of a lake. Rob is across the lake and he makes a 108 degree angle between Tom and Steve. Steve makes a 39 degree angle between Tom and Rob. How far is Tom from Rob? Example

8-2 Law of Sines

Try this Solve ΔABC if a = 50, c = 65 and A = 57º What happened? A b c a

A b c a A b c a A b c a A b c a

A b c a A b c a A b c a A b c a

How do we deal with this? When there are 2 triangles formed the B angles will be Supplementary. (Think Iso Triangle) A B B C C a a b

What is the process to follow? If SSA triangle (given 1 angle) 1._______________________ (csinA) 2.If only 1 ________________________ 3.If there are 2 triangles, ____________ 4.________________________________ ________________________________. 5.________________________________ ________________________________

Example Solve for B and c: if A=53; a=12; and b=15

Examples 1.If you solved it regular first and get “error” or “E” as a solution – that means that there is no triangle possible. **Good one to remember!!

2. Solve for ΔABC if c = 65, a = 60 and A = 57º