Transcript p.-6-notes—Trig-for-packet

Opp Leg
Sin 
Hyp
Adj Leg
Cos 
Hyp
Opp Leg
Tan 
Adj Leg
hypotenuse

adjacent
opposite
opposite
Using a Calculator
3
SinB 
8
SinB  .375
On the calculator enter 0.375 the hit the
“2nd” button and then the “Sin” button.
Sin 1 0.375  22.02
The number 22.02 should be displayed.
This is the angle that has a Sin value of
0.375
Then, that means
3
8
B
On a graphics calculators you
will enter it just like it reads in
the equation.
Sin1  0.375
B  22.02
Then you can calculate the
angle value.
Problem-Solving Strategies
Scenario 1) You are given 2 sides of the triangle.
Find the other side and the two acute angles.
B
G
c
13
OR
15
C
A
C
20
1A. Use the Pythagorean
theorem to find the 3rd side.
c 2  152  202
c  25
15
20
 15 
A  Tan 1  
 20 
A  36.9
B  53.1
TanA 
1B. Use an inverse trig function to
get an angle. Then use that angle
to calculate the 3rd angle. Sum of
the angles = 180º
k
K
12
k 2  122  132
k  25
12
13
 12 
K  Cos 1  
 13 
K  22.6
G  67.4
CosK 
Problem-Solving Strategies
Scenario 2) You are given an
angle and a side.
Find the other angle and the
two other sides.
2A. Use the sum of the
angles to get the 3rd angle.
2B. Use 2 different trig ratios from
the 3rd angle to get each of
the other two sides.
B
26
51
a
C
A
b
A  180 (90 51)
A  39
b
Sin39 
26
0.6293  26  b
a
Cos39 
26
0.7771 26  a
16.4  b
20.2  a
Angle of Elevation/Depression
Sometimes when we use right triangles to model real-life situations, we
use the terms angle of elevation and angle of depression.
If you are standing on the ground and looking up at a hot air balloon, the
angle that you look up from ground level is called the angle of elevation.
If someone is in the hot air balloon and looks down to the ground to see
you, the angle that they have to lower their eyes, from looking straight
ahead, is called the angle of depression.
Balloon
Angle of
depression
Angle of
elevation
You
Angle of Elevation/Depression
If you look up 15º to see the balloon, then the person in the
balloon has to look down 15º to see you on the ground.
Angle of elevation = Angle of depression.
Balloon
Angle of depression = 15º
Angle of
elevation= 15º
You
Notice that in this situation, the one of the legs that forms the
right angle is also the height of the balloon.