Download Lesson 7-4 Right Triangle Trigonometry

Lesson 7-4
Right Triangle
Trigonometry
Lesson 7-4 Right Triangle
Trigonometry
1
In right triangles :

The segment across from the right angle ( AC ) is labeled the hypotenuse
“Hyp.”.
A
Hyp.
Opp.
Angle of Perspective
C
B
Adj.



The “angle of perspective” determines how to label the sides.
Segment opposite from the Angle of Perspective( AB ) is labeled “Opp.”
Segment adjacent to (next to) the Angle of Perspective ( BC ) is labeled
“Adj.”.
* The angle of Perspective is never the right angle.
Lesson 7-4 Right Triangle
Trigonometry
2
Labeling sides depends on the Angle of Perspective
If
A
is the Angle of Perspective then ……
Angle of Perspective
AC  Hyp
A
Hyp.
Adj.
B
Opp.
C
BC  Opp
AB  Adj
*”Opp.” means segment opposite from Angle of Perspective
“Adj.” means segment adjacent from Angle of Perspective
Lesson 7-4 Right Triangle
Trigonometry
3
If the Angle of Perspective is
A
then
A
Hyp
C
Adj
B
then
A
Hyp
Opp
Opp
C
B
Adj
C
AC  Hyp
AC  Hyp
BC  Opp
AB  Opp
AB  Adj
BC  Adj
Lesson 7-4 Right Triangle
Trigonometry
4
Trigonometry Ratios
If C is the Angle of Perspective then …...
Sin
C =
A
Opp
Hyp
Cos C =
Adj
Hyp
tan C =
Opp
Adj
Hyp
Opp
B
Adj
C
Angle of Perspective
Lesson 7-4 Right Triangle
Trigonometry
5
Example: Find the value of x.
Step 1: Mark the “Angle of Perspective”.
Step 2: Label the sides (Hyp / Opp / Adj).
Step 3: Select a trigonometry ratio (sin/ cos / tan).
Opp
Sin  = Hyp
Step 4: Substitute the values into the equation.
x
Sin 25 =
A
opp
Hyp
12 cm
x
25
B
12
Angle of
Perspective
C
Adj
Step 5: Solve the equation : Change Sin 25 into a decimal. Cross multiply and solve.
0.4226 =
1
x
12
x = (0.4226) (12)
x = 5.07 cm
Lesson 7-4 Right Triangle
Trigonometry
6
Solving Trigonometric Equations
There are only three possibilities for the placement of the variable ‘x”.
Sin  =
Opp
Hyp
Sin X =
A
A
12 cm
25 cm
x
B
B
12
25
Sin 25
=
= 0.48
0.4226 =
x
12
Sin X =
Sin X
25
X = Sin 1 (0.48)
X = 28.6854
1
x
12
Sin 
x = 5.04 cm
Lesson 7-4 Right Triangle
Trigonometry
25
Sin 25
=
0.4226
=
1
x =
Opp
x
x
B
C
x = (12) (0.4226)
=
A
12 cm
12 cm
x
C
x
Hyp
12
x
12
x
12
0.4226
x = 28.4 cm
7
C