1. Right Triangle Trigonometry
Lesson 7-4
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.
Hyp.
Opp.
Angle of Perspective
Adj.

3. Labeling sides depends on the Angle of PerspectiveIf
is the Angle of Perspective then ……
Angle of Perspective
Hyp.
Adj.
Opp.
*”Opp.” means segment opposite from Angle of Perspective
“Adj.” means segment adjacent from Angle of Perspective

4. If the Angle of Perspective is
then
then
Hyp
Adj
Hyp
Opp
Opp
Adj

5. Trigonometry Ratios If is the Angle of Perspective then …... Sin =
Cos =
tan =
Hyp
Opp
Adj
Angle of Perspective

6. 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 =
Step 5: Solve the equation : Change Sin 25 into a decimal. Cross multiply and solve.
Hyp
opp
Angle of Perspective
Adj
x = (0.4226) (12)
x = 5.07 cm =

7. Solving Trigonometric Equations
There are only three possibilities for the placement of the variable ‘x”.
Sin =
Sin =
Sin =
Sin =
Sin =
Sin = =
Sin = 0.48 =
X = Sin (0.48)
x =
x = (12) (0.4226)
x = 5.04 cm
X =
x = 28.4 cm

8. Thanks for coming!