Download Make sure you know how to find sin/cos/tan

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.
B
c
A
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:
• _________________________________
• _________________________________
B
c
A
a
b
C
____________________
____________________
____________________
B
c
Area Formula
1
A   by
2
a
y
A
x
b
C
1
A   bc sin A
2
1
A   ac sinB
2
1
A   absinC
2
Heron’s Formula
•Used to find areas of triangles when all
sides are given (SSS)
____________________
____________________
Example
B
Find the area of the triangle
1
A   bc sin A
2
8
C
101
12
A
Example Heron’s
1. Given ΔABC with a = 3, b = 4 and c = 5, find
the area using Heron’s Formula.
A  s(s  a)(s  b)(s  c)
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.
B
c
A
a
b
C
Law of Sines
____________________
Examples
1. Solve ΔABC if a = 5, B= 75º and
C = 41º. A=64º
Example
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?
8-2 Law of Sines
Try this
Solve ΔABC if a = 50, c = 65 and A = 57º
What happened?
a
c
A
b
a
c
A
c
A
b
c
a
b
a
c
A
b
A
a
b
a
c
A
c
A
b
c
a
b
a
c
A
b
A
a
b
How do we deal with this?
When there are 2 triangles formed the B
angles will be Supplementary. (Think Iso
Triangle)
C
C
b
A
a
B
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