CK-12 Geometry Concepts

http://www.ck12.org Chapter 8. Right Triangle Trigonometry

cos 20◦=

a

10

sin 70◦=

a

10

10 ·cos 20◦=a 10 ·sin 70◦=a

a≈ 9. 4 a≈ 9. 4

sin 20◦=

b

10

cos 70◦=

b

10

10 ·sin 20◦=b 10 ·cos 70◦=b

b≈ 3. 4 b≈ 3. 4

Vocabulary

Trigonometryis the study of the relationships between the sides and angles of right triangles. The legs are called
adjacentoroppositedepending on whichacuteangle is being used. The three trigonometric (or trig) ratios are
sine,cosine, andtangent.

Guided Practice

1. What is tan 45◦?


2. Find the length of the missing sides and round your answers to the nearest tenth:.


3. Find the length of the missing sides and round your answers to the nearest tenth:.

Answers:

1. Using your calculator, you should find that tan 45◦=1?


2. Use tangent forxand cosine fory.

tan 28◦=

x

11

cos 28◦=

11

y

11 ·tan 28◦=x

11

cos 28◦

=y

x≈ 5. 8 y≈ 12. 5

3. Use tangent foryand cosine forx.

tan 40◦=

y

16

cos 40◦=

16

x

16 ·tan 40◦=y

16

cos 40◦

=x

y≈ 13. 4 x≈ 20. 9

Practice

Use your calculator to find the value of each trig function below. Round to four decimal places.

1. sin 24◦