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```Warm-Up: Solve each equation
1)
x
0.875 
18
2)
24
 0.5
y
3)
y
 0.96
25
4) 0.866x = 12
5)
0.5x = 18
1)
2)
3)
4)
15.75
48
24
13.9
5) 36
Students will define sine, cosine, and tangent ratios in
right triangles.
Trigonometric Ratios
 The relationships between the angles and the sides of a
right triangle.
Trignometric Ratios
How do I remember this?
Three basic ratios:
• sine (sin), cosine (cos), tangent (tan)
Trigonometric Ratios Theorem
 Let ABC be a right triangle. The sine, the cosine, and
the tangent of the acute angle A are defined as
B
follows:
a
opposite
 sin A =
c
hypotenuse
 cos A =

 tan A =

hypotenuse

opposite

c
b
c
a
b
A
a
b
C
It is known that a hill frequently use for sled riding
has an angle of elevation of 300 at its bottom. If the
length of a sledder’s ride is 52.6 feet estimate the
height of the hill.
h
sin 30 
52.6
52.6
0
52.6  sin 30  h
(52.6)  (0.5)  h
0
26.3  h
h
300
You want to find the height of a tower used to
transmit cellular phone calls. You stand 100 feet
away from the tower and measure the angle of
elevation to be 400. How high is the tower?
t
tan 40 
100
0
tower
100  tan 40 0  t
(100)  .8391  t
84 ft  t
you
400
100 ft

Practice Time!
sin A 
12
 .8
15

x
sin 50 
15
x  11.5
cos A 
9
 .6
15

sin B 
9
 .6
15
cos B 
12
 .8
15

5
cos63 
x
x  11
x
cos 38 
21
x  16.5
```