CK-12 Geometry-Concepts

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

242 +AB^2 = 302

576 +AB^2 = 900

AB^2 = 324

AB=

√

324 = 18

m^6 B: Use the inverse sine ratio.

sinB=

24

30

=

4

5

sin−^1

(

4

5

)

= 53. 1 ◦=m^6 B

m^6 C: Use the inverse cosine ratio.

cosC=

24

30

=

4

5

cos−^1

(

4

5

)

= 36. 9 ◦=m^6 C

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52522

CK-12 Foundation: Chapter8InverseTrigonometricRatiosB

Concept Problem Revisited

To find the escalator’s angle of elevation, we need to use the inverse sine ratio.

sin−^1

(

115

230

)

= 30 ◦ The angle of elevation is 30◦.

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 aresine,
cosine, andtangent. Theinversetrig ratios, sin−^1 ,cos−^1 , and tan−^1 , allow us to find missing angles when we are
given sides.