lesson 7-5 right triangle trigonometry 1 lesson 7-5 right triangle trigonometry
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Lesson 7-5 Right Triangle Trigonometry
1
Lesson 7-5
Right Triangle
Trigonometry
Lesson 7-5 Right Triangle Trigonometry
2
In right triangles : The segment across from the right angle ( ) is labeled the hypotenuse
“Hyp.”.
The “angle of perspective” determines how to label the sides. Segment opposite from the Angle of Perspective( ) is labeled “Opp.” Segment adjacent to (next to) the Angle of Perspective ( ) is labeled
“Adj.”.
* The angle of Perspective is never the right angle.
AC
A
B C
Hyp.Angle of PerspectiveOpp.
Adj.
AB
BC
Lesson 7-5 Right Triangle Trigonometry
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Labeling sides depends on the Angle of Perspective
A
A
B C
Angle of Perspective Hyp.
Opp.
Adj.
If is the Angle of Perspective then ……
AC Hyp
BC Opp
AB Adj
*”Opp.” means segment opposite from Angle of Perspective
“Adj.” means segment adjacent from Angle of Perspective
Lesson 7-5 Right Triangle Trigonometry
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If the Angle of Perspective is
CA then
AC Hyp
BC Opp
AB Adj
A
B COpp
HypAdj
thenA
B C
Opp
Adj
Hyp
AC Hyp
AB Opp
BC Adj
Lesson 7-5 Right Triangle Trigonometry
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Trigonometry Ratios
If is the Angle of Perspective then …...
Sin =
Cos =
tan =
C
A
B C
Angle of Perspective
COpp
Hyp
C Adj
Hyp
C Opp
Adj
OppHyp
Adj
Lesson 7-5 Right Triangle Trigonometry
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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).
Sin =
Step 4: Substitute the values into the equation.
Sin 25 =
Step 5: Solve the equation : Change Sin 25 into a decimal. Cross multiply and solve.
Opp
Hyp
12
x
x12 cm
25
A
B C
Angle of Perspective
Hypopp
Adj
12
x0.4226
1x = (0.4226) (12)
x = 5.07 cm=
Lesson 7-5 Right Triangle Trigonometry
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Solving Trigonometric Equations
There are only three possibilities for the placement of the variable ‘x”.
XSin = Opp
Hyp Sin = x
HypSin = Opp
x
x12 cm
25
A
B C
x12 cm
25
A
B C
25 cm
x
12 cm
A
B C
Sin = X12
25
Sin = 0.48X
X = Sin (0.48)1
X = 28.6854
Sin 25 =
12
x
1x = (12) (0.4226)
x = 5.04 cm
0.4226 = 12
x
Sin 25 = 12
x
0.4226 = 12
x1
x = 12
0.4226
x = 28.4 cm