Download 13.1 Use Trigonometry with Right Triangles

13.1 Use Trigonometry with Right Triangles
Right Triangle Trigonometry
C
b hypotenuse
leg a
B
c
leg
A
Trigonometry Functions: SOH – CAH – TOA
O
H
Sine: sin = /H
Cosine: cos = A/H
Tangent: tan = O/A
Cosecant: csc = /O
Secant: sec = H/A
Cotangent: cot = A/O
Reciprocal Relationships
csc = 1/sin
sec = 1/cos
cot = 1/tan
Evaluate the six trigonometric functions for the angle 
sin  = ________ cos  = ________ tan  = _________
7

csc  = ________ sec  = ________ cot  = _________
24
Special Triangles
30 - 60 - 90
B
30 Degrees
sin 30 = ______
cos 30 = ______
tan 30 = ______
csc 30 = ______
sec 30 = ______
cot 30 = ______
30 30
√3
2
2
60
A
60
1
D
1
60 Degrees
sin 60 = ______
cos 60 = ______
tan 60 = ______
csc 60 = ______
sec 60 = ______
cot 60 = ______
C
A
45 - 45 - 90
45 Degrees
45º
√2
1
45º
C
1
B
sin 45 = _____
cos 45 = _____
tan 45 = _____
csc 45 = _____
sec 45 = _____
cot 45 = _____
Use a right triangle to find the values of all of the trigonometry functions of 
Given: sin  = 1/3
cos  = ________
tan  = ________
Find an unknown side length of a right triangle
Find the exact value for x in the right triangle below.
6
x
45
x = ____________________
Use a calculator to solve a right triangle
Solve Triangle ABC.
B
B = ______________________
c = 20
a = ______________________
a
b = ______________________
54
A
b
C
Angle of elevation
From a point on the ground 28 feet from the base of a flagpole, the angle of
elevation to the top of the flagpole is 63. Estimate the height of the flagpole.