Chapter 8-4 part 2
Trigonometry
Objective: I will find trigonometric ratios using
right angle triangles
Use Trigonometric Ratios to Find a Length
EXERCISING A fitness trainer sets the incline on a
treadmill to 7°. The walking surface is 5 feet long.
Approximately how many inches did the trainer raise
the end of the treadmill from the floor?
=60 in
Let y be the height of the
treadmill from the floor in
inches. The length of the
treadmill is 5 feet, or 60 inches.
opposite
sin 7 
hypotenuse
y
.1219 
60
 y 
60(.1219 )   60
 60 
y =7.314 in
Answer: The treadmill is about 7.3 inches high.
CONSTRUCTION The bottom of a handicap ramp is
15 feet from the entrance of a building. If the angle of
the ramp is about 4.8°, how high does the ramp rise
off the ground to the nearest inch?
A. 1 in.
B. 11 in.
C. 16 in.
1.
2.
3.
4.
D. 15 in.
0%
A
B
C
D
A
B
C
D
Finding Missing Angle Measures
• Decide which Trig function to use based on
the missing angle measure and the two
given sides
• Substitute the given sides and the unknown
variable into the function’s equation
• Calculate the value of the ratio
• Use the trig table to find the angle measure
nearest the ratio value
Quick Examples (using Trig Tables)
• If Sin A = .3256, what is the mA?
= 19º
• If Tan A = 4.3 , what is the mA?
≈ 77º
7
• If Cos A = , what is the mA?
9
≈ 39º
3
• If Sin A = , what is the mA?
4
≈ 48.5º
Example #1
Solve for angle A
A
5
SinA 
15
SinA  .3333
Hyp
15 in
C
SOH-CAH-TOA
Opp
5 in
m  A  19.5
B
Example #1
Solve
for
angle
B
A
SOH-CAH-TOA
5
CosB 
15
CosB  .3333
Hyp
15 in
C
Adj
5 in
m  B  70 .5 
B
Example #2
Solve for angle R
7
TanR 
10
TanR  .7 
R
m  R  35 .0 
Adj
10
T
SOH-CAH-TOA
Opp
7
S
Example #2
Solve for angle S
SOH-CAH-TOA
10
TanS 
7
R
TanS  1.4286
m  S  55 
Opp
10
T
Adj
7
S
Ask yourself:
In relation to the angle, what
pieces do I have?
34°
15 cm
Opposite and hypotenuse
Ask yourself:
x cm
What trig ratio uses
Opposite and Hypotenuse?
SINE
Set up the equation and solve:
(15) Sin 34 = x (15)
15
(15)Sin 34 = x
8.39 cm = x
Ask yourself:
In relation to the angle, what
pieces do I have?
53°
12 cm
Opposite and adjacent
x cm
Ask yourself:
What trig ratio uses
Opposite and adjacent?
tangent
Set up the equation and solve:
(12)Tan 53 = x (12)
12
(12)tan 53 = x
15.92 cm = x
x cm
Ask yourself:
In relation to the angle, what
pieces do I have?
Adjacent and hypotenuse
68°
18 cm
Ask yourself:
What trig ratio uses
adjacent and hypotnuse?
cosine
Set up the equation and solve:
(x) Cos 68 = 18(x)
x
(x)Cos
18
_____68 =_____
cos 68 cos 68
X = 18
X = 48.05 cm
cos 68
42 cm
22 cm
θ
This time, you’re looking for theta.
Ask yourself:
In relation to the angle, what pieces
Opposite and hypotenuse
do I have?
Ask yourself:
What trig ratio uses opposite
and hypotenuse? sine
Set up the equation (remember you’re looking for theta):
Sin θ = 22
42
Remember to use the inverse function
when you find theta
Sin -1 22 = θ
42
31.59°= θ
Ex.
A surveyor is standing 50 feet from the base of
a large tree. The surveyor measures the
angle of elevation to the top of the tree as
71.5°. How tall is the tree?
tan
71.5°
?
50
71.5
°
Opp

Hyp
y

50
tan
71.5°
y = 50 (tan 71.5°)
y = 50 (2.98868)
y  149.4 ft
Ex. 5
A person is 200 yards from a river. Rather than
walk directly to the river, the person walks along a
straight path to the river’s edge at a 60° angle.
How far must the person walk to reach the river’s
edge?
cos 60°
x (cos 60°) = 200
200
60°
x
x
X = 400 yards
EXIT TICKET
θ
22 cm
17 cm
You’re still looking for theta.
θ
Ask yourself:
22 cm
17 cm
What trig ratio uses the parts I
was given? tangent
Set it up, solve it, tell me what you get.
tan θ = 17
22
tan -1 17 = θ
22
37.69°= θ