Hypotenuse
(always across from the
right angle)
opposite side
(always across
from ϴ)
Theta - reference angle
ϴ
adjacent side
(always next to ϴ)
To determine which side is opposite
and which side is adjacent:
Pretend you are standing at the angle
you know
The angle when you look across is the
opposite side
What are trig ratios:
Used to find missing sides or angles in right triangles
Fractions which relate one side of a triangle to another
Need to know one side and one of the acute angles or two sides
sin Θ =
The angle next to you is the adjacent
side
opposite
O
=
hypotenuse H
cos Θ =
adjacent
A
=
hypotenuse H
Steps to solve problems with trig ratios:
1. Draw the picture, if not given
2. Identify ϴ
3. Identify the known value(s)
4. Identify the wanted value(s)
5. Identify which ratio to use
6. Fill in the proportion with known values
7. Solve the proportion for the unknown value
tan Θ =
opposite
O
=
adjacent
A
Write the all three trig ratios for each of the following triangles. Round to 4 decimal places.
Example 1:
B
sin A =
28
= .5283
53
cos A =
45
= .8491
53
53
28
hypotenuse
opposite
tan A =
ϴ
C
28
= .6222
45
A
45
adjacent
Example 2:
C
42
sin A =
40
adjacent
40
= .6897
58
opposite
tan A =
ϴ
A
B
58
42
= .7241
58
cos A =
40
= . 9524
42
hypotenuse
Example 3:
A
hypotenuse
sin B =
65
B
ϴ
56
= .8615
65
56
opposite
33
adjacent
tan B =
cos B =
33
= .5077
65
56
= 1.6970
33
C
Using Your Calculator:
Make sure the calculator is set to degrees (not radians)
Use sin, cos and tan if you are looking for a side
Use sin-1, cos-1 and tan-1 if you are looking for an angle
Use your calculator to find the given value to 4 decimal places:
1. sin 35° = .5736
2. cos 35° = .8192
3. tan 35° = .7002
If sin ϴ = .6691, what is ϴ?
sin-1 (.6691) = 42°
If tan ϴ = 2.4751, what is ϴ?
tan-1 (2.4751) = 68°
Example 1:
en
hypot
u se
Skateboard Ramp.
et
1 5 fe
x feet
Find the height and length of the
base of the ramp shown.
opposite
27°
y feet
adjacent
Height:
ϴ = 27°
Know - hypotenuse = 15 feet
Want - opposite = x feet
Use sin ϴ = opposite
hypotenuse
x
(15)
15
15(.4540) = x
6.8 feet = x
(15) sin 27 ° =
Example 2:
Lamppost.
Find the height of the
lamppost to the
nearest inch.
Length:
ϴ = 27°
Know - hypotenuse = 15 feet
Want - adjacent = y feet
Use cos ϴ = adjacent
hypotenuse
y
(15)
15
15(.8910) = y
13.4 feet = y
(15) cos 27° =
Ladder.
If a 28 foot long ladder is placed
against a house where the base of
the ladder is 19 feet from the
house. What is the angle the
ladder creates with the ground?
Example 3:
28 ft
ϴ
19 ft
h
68°
38 in.
Height:
ϴ = 68°
Know - adjacent = 38 inches
Want - opposite = h inches
Use tan ϴ = opposite
adjacent
h
(38)
38
38(2.4750) = h
(38) tan 68 ° =
94 inches = h
Angle of Elevation:
Know - adjacent = 19 feet
Know - hypotenuse = 28 feet
Want - ϴ
Use cos ϴ = adjacent
hypotenuse
19
28
cos ϴ = .6786
cos-1 (.6786) = 47.3°
ϴ = 47.3°
cos Θ =