CK-12 Geometry - Second Edition

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

Angle of Elevation:The angle measure from the horizon or horizontal line, up.

Example 7:An inquisitive math student is standing 25 feet from the base of the Washington Monument. The angle
of elevation from her horizontal line of sight is 87. 4 ◦. If her “eye height” is 5ft, how tall is the monument?

Solution:We can find the height of the monument by using the tangent ratio and then adding the eye height of the
student.

tan 87. 4 ◦=

h

25

h= 25 ·tan 87. 4 ◦= 550. 54

Adding 5 ft, the total height of the Washington Monument is 555.54 ft.

According to Wikipedia, the actual height of the monument is 555.427 ft.

Know What? RevisitedTo 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

Review Questions

Use the diagram to fill in the blanks below.