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4.8
Applications and
Models
Solve the right triangle.
B
a
C
c
B = ? = 90 – 34.2 = 55.8°
a
tan 34.2 =
a = 13.18
19.4
o
34.2°
b = 19.4
19.4
A cos 34.2° =
c
! 23.46
h 40’
If the ladder is 40’ long
and the angle of elevation
is 42 °, how high up is the
fireman?
42°
h
sin 42° =
40
! 26.77 ft.
At a point 200 feet from the base of a building, the angle
of elevation to the bottom of a smokestack is 35°, while
the angle to the top is 53°. Find the height, s, of the
smokestack alone.
x
tan 35° =
200
x+s
tan 53° =
s
200
53°
x
35°
200 ft.
x ! 140.04
x + s ! 265.41
265.41
-140.04
125.37 ft.
Trigonometry and Bearings
N
N
80°
W
E
S
35°
S 35° E
W
E
S
N 80° W
A ship leaves port at noon and heads due west at 20
knots (nautical miles per hour). At 2 P.M. , to avoid
a storm, the ship changes course to N 54° W. Find the
ship’s bearing and distance from the port of departure
at 3 P.M..
Now find angle A.
11.76
tan A =
16.18 + 40
D
c
! 11.82°
N 78.18° W
b =11.76
20 nm
54°
36°
d = 16.18
B
! 11.82°
2(20) = 40 nm
A
Find c.
c = 57.4 nm