Transcript PCH Notes 4.3ax

Date:
4.3(a) Notes: Trig. Ratios
Lesson Objective: Use right triangles to
evaluate trig functions.
CCSS: F-TF Extend the domain of trigonometric
functions using the unit circle.
You will need: calculator
Lesson 1: Trig. Definitions
Trigonometric (trig) Ratio: A ratio of 2 sides of
a right triangle.
Reference Angle: The acute angle we are
referring to or are using.
Opposite Leg: The leg across from the / that is
not the hypotenuse.
Adjacent Leg: The leg next to the / that is not
the hypotenuse.
Hypotenuse: The side opposite the right / .
Lesson 1: Trig. Definitions
BC is _________________ / A.
AB is ________________ / A.
AC is the ___________________.
A
B
C
Lesson 2: SOH-CAH-TOA Game
Draw the figure. Choose the correct answer.
Write each question and answer in your notes.
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
A.
Opposite / X
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
B.
Adjacent to / X
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
C.
Hypotenuse
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
D.
Adjacent to Leg 1
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
E.
Opposite / Y
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
F.
Opposite Leg 1
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
G.
Opposite / Z
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
H.
Adjacent to Leg 3
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
I.
Adjacent to / Z
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
J.
Opposite / Y
Z
1
Y
2
3
X
Lesson 2: SOH-CAH-TOA Game
K.
Opposite Leg 3
Z
1
Y
2
3
X
Lesson 3: Trig. Ratios
“SOH”
Lesson 3: Trig. Ratios
“CAH”
Lesson 3: Trig. Ratios
“TOA”
Lesson 3: Trig. Ratios
“SOH-CAH-TOA”
COSECANT = 1 = Hypotenuse
csc
SIN
Opposite
SECANT = 1 = Hypotenuse
sec
COS
Adjacent
COTANGENT = 1 = Adjacent
cot
TAN Opposite
Lesson 3: Trig. Ratios
Find the values of the 6 trig. functions of θ.
Lesson 4: Angle of Elevation and Depression
Lesson 4: Angle of Elevation and Depression
A. Suppose the car is 150 feet from the
building and the observer’s angle of depression is 40°. What is the distance of the line of
sight below the observer?
Lesson 4: Angle of Elevation and Depression
B Sighting the top of a building, a surveyor
measured the angle of elevation to be 22°.
The transit through which the surveyor sights
the building’s angle of elevation is 5 feet above
the ground and 300 feet from the building.
Draw a diagram, then find the building’s
height.
4.3(a): Do I Get It? Yes or No
1. Find the values of the 6 trig. functions
of the other acute angle, β,.
4.3(a): Do I Get It? Continued
2. A surveyor is
standing 115 feet
from the base of the
Washington Monument. The surveyor
measures the angle
of elevation to the
top of the monument as 78.3°. How
Tall is the Washington
Monument?
4.3(a): Do I Get It? Continued
3.
Find the length c of the skateboard ramp.