49.
Let
x
represent the vertical change of the plane
after climbing at a constant angle of 3° for 60
ground miles.
tan3°
6
x
0
60tan3°
x
KEYSTROKES:
60
3
x
3.1
The plane is about 3.1
1 or 4.1 miles above
sea level.
50.
Let
x
represent the maximum height.
sin75°
¬
2
x
0
20sin75°
¬
x
KEYSTROKES:
20
75
x
19.32
The ladder can reach a maximum height of about
19.32 feet.
51.
Let
x
represent the distance from the base of the
ladder to the building.
cos75°
2
x
0
20cos75°
x
KEYSTROKES:
20
75
x
5.18
The base of the ladder is about 5.18 feet from the
building.
52.
Explore:
You know the coordinates of the vertices
of a right triangle and that
C
is the right angle.
You need to find the measure of one of the angles.
Plan:
Use the Distance Formula to find the
measure of each side. Then use one of the
trigonometric ratios to write an equation. Use the
inverse to find
m
J
.
Solve:
JC
(2
2)
2
(
2
2)
2
0
16 or 4
CL
(7
2)
2
[
2
(
2)]
2
25
0 or 5
JL
(7
2)
2
(
2
2)
2
25
16
41
tan
J
C
JC
L
tan
J
5
4
J
tan
1
5
4
KEYSTROKES:
[TAN
1
] 5
4
m
J
51.34019175
The measure of
J
is about 51.3.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Trigonometry, Hypotenuse, 3°, 4.1 miles, 5.18 feet

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