Download 44 Instructional Material

Lesson 7-44
Right Triangle
Trigonometry
LESSON 7-4 RIGHT TRIANGLE
1
In right triangles :
The segment across from the right angle ( AC ) is labeled the hypotenuse.
A
Angle of Perspective
B
C
The “angle of perspective” determines how to label the sides.
* The angle of Perspective is never the right angle.
LESSON 7-4 RIGHT TRIANGLE
2
Labeling sides depends on the Angle of Perspective
If
A
is the Angle of Perspective then ……
Angle of Perspective
A
Hyp.
Adj.
B
AC  Hyp
BC  Opp
AB  Adj
Opp.
C
“Opp.” means segment opposite from Angle of Perspective
“Adj.” means segment adjacent from Angle of Perspective
LESSON 7-4 RIGHT TRIANGLE
3
If the Angle of Perspective is
A
then
A
Hyp
C
Adj
B
then
A
Hyp
Opp
Opp
C
B
Adj
AC  Hyp
AC  Hyp
BC  Opp
AB  Opp
AB  Adj
BC  Adj
LESSON 7-4 RIGHT TRIANGLE
C
4
Trigonometry Ratios
If C is the Angle of Perspective then …...
Sin C =
Cos C =
tan C =
Opp
Hyp
Adj
Hyp
Opp
Adj
LESSON 7-4 RIGHT TRIANGLE
A
Hyp
Opp
B
C
Adj
Angle of Perspective
5
SOH – CAH - TOA
http://www.youtube.com/watch?v=PIWJo5uK3Fo
*warning…. this is annoying
LESSON 7-4 RIGHT TRIANGLE
6
Examples
Use LMN to find sin L, cos L, tan L, sin M, cos M, and tan M. Express each ratio as
a fraction and as a decimal to the nearest hundredth.
Finding sin, cos, and tan using the
calculator
Be sure your calculator is in degree mode.
Examples
Use a calculator to find each value. Round to the nearest ten-thousandth.
sin 94.4
tan 28.5
cos 58.4
In calculator:
◦ shift sin
◦ Shift cos
◦ Shift tan
Examples
 Find the measure of each acute angle to the nearest tenth of a degree.
sin B = 0.7843
tan A = 0. 2386
cos R = 0. 6461
Example: Find the value of x.
Step 1: Mark the “Angle of Perspective”.
A
Step 2: Label the sides (Hyp / Opp / Adj).
opp
Step 3: Select a trigonometry ratio (sin/ cos / tan).
Sin  =
12 cm
x
Opp
Hyp
25
B
Step 4: Substitute the values into the equation.
Sin 25 =
Hyp
Angle of
Perspective
C
Adj
x
12
Step 5: Solve the equation : Change Sin 25 into a decimal. Multiply and solve.
x
0.4226 =
12
x = (0.4226) (12)
x = 5.07 cm
LESSON 7-4 RIGHT TRIANGLE
12
Solving Trigonometric Equations
There are only three possibilities for the placement of the variable ‘x”.
Opp
Hyp
Sin (x) =
Sin  =
A
A
12 cm
25 cm
x
B
Sin (x) =
x
C
12
25
Sin (x) = 0.48
X = Sin 1 (0.48)
X = 28.6854
B
x
Hyp
x
Sin 25 =
12
0.4226 = x
12
=
A
C
x = (12) (0.4226)
x = 5.04 cm
LESSON 7-4 RIGHT TRIANGLE
25
B
Sin 25
0.4226
Opp
x
x
12 cm
12 cm
25
Sin 
=
=
C
12
x
12
x
0.4226 x = 12
x = 28.4 cm
13
Angle of Elevation
The angle between the line of sight and a horizontal when an
observer looks upward.
Angle of Depression
The angle between the line of sight and a horizontal when an
observer looks downward.
Examples
Find x. Round to the nearest tenth.
Examples
Find x. Round to the nearest tenth.
Examples
Find x. Round to the nearest tenth.
In summary…
https://www.youtube.com/watch?v=t2uPYYLH4Zo
LESSON 7-4 RIGHT TRIANGLE TRIGONOMETRY
19