Analysis
Trigonometry Applications II
Name________________
Date_________________
SOLUTIONS AT THE END OF PACKET
1. A regular pentagon is inscribed in a circle, shown below.
A
3
O
3
B
a) Find the measure of AOB in the figure above.
b) Find the measure of side AB
c) Find the area of triangle AOB
2. A person flying a kite holds the string 4 feet above ground level. The
string of the kite is taut and makes an angle of 60° with the horizontal.
Approximate the height of the kite above ground level if 500 feet of
string is payed out.
3. Find the area of a triangle with side lengths 5 and 8 and an included angle
of 38°.
4. A person is 200 yards from a river. Rather than walking directly to the
river, the person walks 400 yards along a straight path to the rivers
edge. Find the acute angle  between this path and the river’s edge.
5. A 65-foot line is used to tether a helium-filled balloon. Because of a
breeze, the line makes an angle of 75 with the ground. What is the
height of the balloon?
6. From an 80-foot observation tower on the coast, a Coast Guard officer
sights a boat in difficulty. The angle of depression of the boat is 3.
How far is the boat from the shoreline?
Analysis
Trigonometry Applications II
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7. A ramp 20 feet in length rises to a loading platform that is 4 feet off
the ground. What is the angle of elevation of the ramp?
8. An airplane at an altitude of 6 miles, is on a flight past that passes
directly over an observer. If  is the angle of elevation from the
observer to the plane, find the distance d from the observer to the plane
when a)  = 30, b)  = 60, c)  = 120.
9. A boat is pulled to port by means of a winch which is located on the dock
10 feet above the deck of the boat. Let X be the angle of elevation and
let s be the length of the rope from the winch to the boat. a) Write X
as a function of s. b) Find X when s = 48 feet and when s = 24 feet.
10. A television camera at ground level is filming the lift-off of a space
shuttle at a point 750 meters from the launch pad. Let X be the angle of
elevation to the shuttle and let s be the height of the shuttle. a) Write
X as a function of s. b) Find X when s = 300 meters and s = 1200 meters.
11. To thank Mr. Cendrowski for the wonderful job he has done with this
year’s Analysis classes, several juniors got together to erect a statue in
his image and place it on the roof of the high school. A student standing
200 feet away from the building looks up at a 27 angle and notices the
statue’s feet. The student then tilts her head back 15 degrees and sees
the top of the statue’s head. How tall is the statue?
12. A plane flying in a straight line passes directly over point A on the ground
and later directly over point B, which is 3 miles from point A. A few
minutes after the plane passes over point B, the angle of elevation from
A to the plane is 43˚ and the angle of elevation from B to the plane is
67˚. How high is the plane at that moment?
C
a
67
43
A
h
3 mi les
B
Mr. John Cendrowski
Analysis
D
Analysis
Trigonometry Applications II
1.
a) 72
b) 3.53
c) 4.28
2.
3.
4.
5.
6.
7.
8.
437.01
12.31
30°
62.79
1526.49
11.54
30°, 12
60°, 6.93
120°, 6.93
 10 
X  sin 1  
s 
9.
10.
11.
12.
48, 12.02
24, 24.62
 s 
X  tan 1 

 750 
300, 21.80
1200, 57.99
78.18
4.63
Mr. John Cendrowski
Analysis
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