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Tangent Ratio
Labelling Right Triangles
Theta: the symbol we will use to represent an
unknown angle. Ө
Ө
Hypotenuse
Adjacent
Opposite
Definitions
Hypotenuse: The longest side of a right
triangle. It is always across from the 90
degree angle.
Adjacent side: Always the side that is attached
to or touching the theta symbol Ө
Opposite Side: Always the side that is across
from the theta symbol. It is not touching Ө
Ex 1) Label the triangle with HYP, ADJ, and
OPP
Hypotenuse
Opposite
Ө
Adjacent
Ex 2) Place Ө in the correct angle.
Adjacent
Opposite
Ө
Hypotenuse
HYP
OPP
Ө
ADJ
Ratios
When
have
right triangle,
and we
have 1 given
Step 1:we
label
theasides
HYP OPP
ADJ
side and 1 given angle, and we need to find the
Step
2: Choose
either
Sin, SIN,
Cos orCOS
Tan or
(depending
missing
sides,
we use
TAN. on
which side is given and which side you need to find)
Step 3: Write out the formula with Sin, Cos or Tan
Step 4: Insert the information that has been given in the
question (the side length and the angle).
Tangent Ratio (TAN)
Tan θ = Opposite side
Adjacent side
If you have a triangle, and you are given a measurement
and a variable for the OPPOSITE SIDE and the
ADJACENT SIDE, then you need to use the TAN
function on your calculator to find the missing side.
Trigonometric Ratios
Tangent Ratio
Step 1: Label sides
Tan A = Opposite
Adjacent
Step 2: Choose Sin, Cos, Tan
Step 3: Write out formula
A
45
ADJ
Step 4: Insert the given
information
(A or Ө is always an angle)
HYP
13cm
Step 5: Find the missing side (x).
Use cross-multiplication
B
C
x cm
OPP
Tan 45o = x cm
13cm
Ex 1) Write an equation that you can use to find
the value of x.
A
OPP
Tan C= Opp
Adj
D
ADJ
Tan 30= x cm
11cm
x
5cm
OPP
F
X cm
30
E
B
30
11 cm
ADJ
C
Tan F= Opp
Adj
Tan 30= 5 cm
x cm
Ex 2) Find Tan A. Keep your answer as a
fraction.
Tan A = Opposite
Adjacent
A
5cm
Tan A= 7cm
5cm
√74 cm
B
ADJ
6√3 cm
6cm
B
OPP
C
7cm
A
12cm
C
Ex 3) Find the value of x.
45
32 cm
15cm
60
x
x
Class Work
Page 560 #1, 2, 4
Page 561 #13-15
Sine and Cosine Ratios
Sine Ratio
If you have a triangle, and you are given a
measurement and a variable for the OPPOSITE
SIDE and the HYPOTENUSE, then you need to
use the SIN function.
Sin Ө = Opposite Side
Hypotenuse
Trigonometric Ratios
Ex 1) Write an equation for Sin A.
Find the value of x.
Sin A = Opp
Hyp
A
Sin 30 = x cm
10 cm
30
10cm
10 cm (Sin 30) = x cm
1/2 x 10 = x
x = 5 cm
B
x cm
C
Ex 1) Write an equation for Sin A. Find the
value of x.
B
X cm
12cm
60
C
A
Cosine Ratio
If you have a triangle, and you are given a
measurement and a variable for the
HYPOTENUSE and the ADJACENT SIDE,
then you need to use the COS function.
Cos Ө = Adjacent Side
Hypotenuse
Trigonometric Ratios
Write an equation for Cos A
A
7cm
B
B
12cm
11cm
C
C
A
5cm
Ex 1) Write an equation for Cos A.
Find the value of x.
A
Cos A = ADJ
HYP
45
7cm
Cos 45 = 7cm
x cm
√2 = 7
2
x
x cm
√2 x = 14
B
C
x=7√2
Ex 1)
Find the value of x. Choose Sin,
Cos or Tan.
B
11cm
6 cm
30
C
A
x cm
Ex 2) Write equations for Sin A and Cos A.
A
15cm
17cm
B
A
8cm
C
10 cm
B
8cm
6 cm
C
Trigonometric Ratios
SOH
CAH
TOA
Sin A = Opp
Hyp
Cos A = Adj
Hyp
Tan A= Opp
Adj
Class Work
• Page 563 #1-3
• Page 564 # 4-6
• Page 566 #11-16