CK-12 Geometry Concepts

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

Concept Problem Revisited

To find the horizontal length and the actual length of the ramp, we need to use the tangent and sine.

tan 5◦=

2

x

sin 5◦=

2

y

x=

2

tan 5◦

= 22. 86 y=

2

sin 5◦

= 22. 95

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. Theangle of depressionis the angle measured down from the horizon or a horizontal
line. Theangle of elevationis the angle measured up from the horizon or a horizontal line.

Guided Practice

1. Mark is flying a kite and realizes that 300 feet of string are out. The angle of the string with the ground is 42. 5 ◦.
   How high is Mark’s kite above the ground?


2. A 20 foot ladder rests against a wall. The base of the ladder is 7 feet from the wall. What angle does the ladder
   make with the ground?


3. A 20 foot ladder rests against a wall. The ladder makes a 55◦angle with the ground. How far from the wall is the
   base of the ladder?

Answers

1. It might help to draw a picture. Then write and solve a trig equation.

sin 42. 5 ◦=

x

300

300 ·sin 42. 5 ◦=x

x≈ 202. 7

The kite is about 202.7 feet off of the ground.

2. It might help to draw a picture.

cosx=

7

20

x=cos−^1

7

20

x≈ 69. 5 ◦

.

3. It might help to draw a picture.