Download Trig-18-Solving Right Triangles

10/22/2013
Right Triangle Trigonometric Ratios
Note:
Right triangle trig ratios are only of acute angles.
Solving Right Triangles
Notations:
Sine of A:
Cosine of A:
Tangent of A:
Cosecant of A:
Secant of A:
Cotangent of A:
Trigonometry
Radnor High School
sin A
cos A
tan A
csc A
sec A
cot A
2
BC
AB
AC
cos A 
AB
BC
B tan A 
AC
A
Right Triangle Trigonometric Ratios
opposite leg
hypotenuse
adjacent leg
cos A 
hypotenuse
opposite leg
tan A 
adjacent leg
sin A 
sin A 
c
b
hypotenuse
opposite leg
hypotenuse
sec A 
adjacent leg
adjacent leg
cot A 
opposite leg
csc A 
a
C
1
sin A
1
sec A 
cos A
1
cot A 
tan A
csc A 
SOHCAHTOA
3
Example 1:
sinA 
4
Example 2:
Find the 6 trig ratios of A and B.
Find the 6 trig ratios of A and B.
A
A
5
C
1
csc A
1
or cosA 
sec A
1
or tanA 
cot A
or
AB
BC
AB
sec A 
AC
AC
cot A 
BC
csc A 
8
12
B
C
5
8
B
6
1
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Example 3:
Using inverse trig ratios on calculator
Find the 6 trig ratios of A and B.
If we know the value of a trig ratio of an acute angle,
we can use the corresponding inverse trig ratio to
find the measure of the angle.
A
4
2
B
C
If sin A  x
then
A  sin 1 ( x)
If cos A  y
then
A  cos 1 ( y )
If tan A  z
then A  tan 1 ( z )
7
8
Example 4:
Solving Right Triangles
Find the measure of angle A if
a) sin A = 0.341
To solve a right triangle is to find all missing side
lengths and missing angle measures from the given
information.
b) cos A = 0.742
c) tan A = 2.347
9
10
Example 5:
Example 6:
Solve the right triangle below.
Solve the right triangle below.
A
A
7
12
C
15
B
C
11
65
B
12
2
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Angles of Elevation or Depression
An angle of elevation or depression is the angle
formed by the line of sight and the horizontal line.
 of depression
Looking
up
Lookingg
down
 of elevation
13
Example 7:
14
Example 8:
Tom knows when he stands 123 feet from the base
of a flagpole, the angle of elevation to the top is 26.
If his eyes are 5 feet 3 inches above the ground, find
the height of the flagpole.
The length of the shadow of a building 34.09 meters
tall is 37.62 meters. Find the angle of elevation of the
sun.
15
16
Example 9:
An airplane is approaching an airport. The pilot
knows that the plane’s altitude is 2000ft and the angle
of depression from plane to the airport is 25. Help
the pilot to find how far the plane is from the airport.
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3