13.1Right TriangleTrigonometry

The Good Stuff

Trigonometric Functions

sinopp

hyp

cosadj

hyp

tanopp

adj

cschyp

opp

sechyp

adj

cotadj

opp

Pythagorean vs. Trigonometry

a

θ

b

c

Using a calculator to find trig values

sin14˚ cos31˚ tan59˚ sec23˚ csc80˚ cot36˚

.2419

.85721.66431.08641.0154

1.3764

Angle of Elevation vs. Angle of Depression

θ

α

Application

10˚

An airplane is flying at an altitude of 30,000 feet is headed toward an airport. To guide the airplane to a safe landing, the airport’s landing system sends radar signals from the runway to the airplane at a 10˚ angle of elevation. How far away is the airplane (measured along the ground) from the airport runway?

30,000 ft

cot 1030000

x

30000 cot 10x

1

30000tan 10

x

30000 5.671x

170100x

Memory work

sinopp

hyp cos

adj

hyp tan

opp

adj

cschyp

opp sec

hyp

adj cot

adj

opp

Memory work

θ sin θ cos θ tan θ csc θ sec θ cot θ

30˚

45˚

60˚3

1

2

1

2

3

2

3

2

2

2

3

3

1

2 2 3

33

22

2

22 3

3

2

3

3

1