Do-Now
1. Use the Pythagorean Theorem to solve the following problem.
Firefighters have a 17 foot extension ladder. In order to reach 15
feet up a building, how far away from the building should the foot
of the ladder be placed?
Convert each fraction to a decimal. Round to four decimal
places.
2. 2
3. 3
4. 8
3
7
8
9.7-9.8: Trigonmetric Ratios
Objective: use sine, cosine and tangent
ratios to find side lengths of triangles
Homework:
9.7-9.8 Practice Worksheet
Trigonometry
• The ratio of lengths of two sides of a
right triangle
• You can only take the sine, cosine, and
tangent of one of the acute angles of
a right triangle.
• Real-life connection: Architecture,
landscaping, construction, etc.
(careers that use math, science and
•
engineering)
Vocabulary to understand:
Hypotenuse
Opposite
Adjacent
X
sin X 
Z
ZY
XY
Y
Finding lengths: Make sure
calculator is in Radian mode
not Degree
Sine (abbreviation: sin)
opposite leg
sin  
hypotenuse
*The opposite side is
always across from the
given angle.
* The hypotenuse is always
the side opposite of the
right angle.
X
sin X 
Z
ZY
sin  X 
XY
ZY
XY
Y
XZ
sin Y 
XY
Cosine (abbreviation: cos)
adjacent leg
cos  
hypotenuse
* The adjacent side is always
next to or attached to the
angle that is identified. It
cannot be the hypotenuse.
X
Z
XZ
cos X 
XY
Y
ZY
cos Y 
XY
Tangent (abbreviation: tan)
opposite leg
tan  
adjacent leg
X
ZY
tan X 
XZ
XZ
tan Y 
ZY
Z
Y
SOHCAHTOA
cos =
A
tan =
5
3
C
4
4
5
2.) sin B  3
5
3
3.) cos A 
5
4.) cos B  4
5
4
5.) tan A 
3
3
6.) tan B 
4
1.) sin A 
sin =
B
Describe how the measures
of two legs are related if
the tangent of one of the
acute angles is = 1.
Use your calculator and round
to the nearest hundredth.
o
1.) sin 43 =
o
2.) cos 72 =
o
3.) tan 35 =
Solve for the variable.
1. Start by asking yourself, what sides are the numbers and
variables in relation to the given angle measure (adjacent
side, opposite side or hypotenuse)?
2. Then ask, which trig function uses the sides you identified?
3. Set up the ratios based on S O H C A H T O A.
opposite
opposite
Solve for the variable.
When the variable is on the bottom, divide
(# ÷ trig function).
When the variable is on the top, multiply
(# x trig function).
Tan 22˚=
3
x
3 ÷ Tan 20 =
Cos 32˚=
b
10
10 x Cos 32 =
Sin 28˚=
a
15
15 x Sin 28 =
Real-life Connection
A surveyor is finding the width of a river for a proposed
bridge. A theodolite is used by the surveyor to measure
angles. The distance from the surveyor to the proposed bridge
site is 40 feet. The surveyor measures a 50 angle to the
bridge site across the river. Find the length of the bridge to
the nearest foot.
Review:
Find the following and write the answers
as fractions in simplest form and as
decimals rounded to the four decimal
places.
1. Sin P =
2. Cos P =
3. Tan P =
Find the lengths of the legs.
Round your answer to four
decimal places.
4.
5.