Download Use a calculator to approximate the value of the trigonometric function

Accelerated Algebra II
W.S. 13.1 - day 3 (Applications)
Name __________________________________
Assign. # ______
Use a calculator to approximate the value of the trigonometric function. Round your result to four
decimal places if you are finding a side and to the nearest second if you are finding an angle.
1.
csc 29
2.
cot 2515’
3.
sec 47
4.
cos  = 0.415
5.
sin  = 0.9573
6.
tan  = 2.2327
7.
csc  = 2.0626
8.
cot  = 0.1228
9.
sec  = 1.5723
To receive credit for the following problems, neatly draw and label an appropriate diagram, write
a trigonometric equation, and find the solution to the problem. Round angles to nearest second
and sides to the nearest 100th.
10.
A medivac helicopter is headed for a hospital a distance of 4 miles away. If the helicopter is
flying at an altitude of a half-mile, what is the angle of depression to the hospital heliport,
300 feet above ground?
11.
The Grouse Mountain ski slope in Avon, Colorado has a vertical height of 1808 feet and
rises at an angle of about 25.2. How long is the ski slope to the nearest 100th of a foot?
Acc. Alg. II -- W. S. 13.1
day 3
Page 2
12.
A train travels 2.5 miles on a straight track which has a grade of 110’. What is the vertical
rise of the train in that distance to the nearest 100th of a mile?
13.
The length of the shadow of a tree is approximately 125 feet when the angle of elevation of
the sun is 33. Approximate the height of the tree to the nearest 100th of a foot.
14.
A radio transmission tower is 200 feet high. How long, to the nearest 100 th of a foot,
should a guy wire be if it is to be attached to the tower 10 feet from the top and is to make
an angle of 21 with the ground?
Acc. Alg. II -- W. S. 13.1
day 3
Page 3
15.
A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted
so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find
the angle of depression to the nearest 10th of a degree of the bottom of the pool. Hint: Draw
your diagram as if you were standing on the bottom looking at the longer side of the pool.
16.
A smokestack stands on top of a building. From a point 200 feet from the base of the
building, the angle of elevation to the bottom of the stack is 35, while the angle of elevation
to the top is 53. Find the height of the smokestack to the nearest 100th of a foot.
17.
An observer 2.5 miles from the launch pad of a space shuttle measures the angle of
elevation to the base of the vehicle to be 28 soon after liftoff. How high is the shuttle at
that instant, to the nearest 100th of a mile if you assume that the shuttle is still moving
vertically.
Acc. Alg. II -- W. S. 13.1
18.
day 3
Page 4
Meteorologist Wendy Stevens uses a theodolite (an angle-measuring device) on a 1-meter tall
tripod to find the height of a weather balloon. She views the balloon at a 44 angle of
elevation. A radio signal from the balloon to the theodolite tells her that the balloon is 1400
meters from her theodolite. Find the height of the balloon to the nearest 100th of a meter.
SCIENCE CONNECTION: Weather balloons carry into the atmosphere what is called a radiosonde, an
instrument with sensors that detect information about wind direction, temperature, air pressure, and
humidity. Twice a day across the world, this upper-air data is transmitted by radio waves to a receiving
station. Meteorologists use the information to forecast the weather.
Determine, withOUT the use of a calculator, whether the statement is true or false. Show all work to
support your answer.
19.
T
F
sin 60 csc 60 = 1
(Hint: Draw & label a 30-60-90 rt. )
20.
T
F
tan csc = sec
(Hint: Use def. of the trig. functions.)
21.
T
F
cot sec sin = 1
(Hint: Use def. of the trig. functions.)
Some Answers – Remember they are never guaranteed!
1)
7)
11)
14)
17)
20)
2.0627
290’4”
 4246.33 ft.
 530.18 ft.
 1.33 mi
T
3)
9)
12)
15)
18)
21)
1.4663
5030’18”
 0.05 mi
 7.7
973.52 m
T
5)
10)
13)
16)
19)
7311’46”
619’20”
 81.18 ft.
 125.37 ft.
T