Download Advanced Algebra with Trigonometry

Advanced Algebra with Trigonometry
Ch 5: “Trigonometric Functions”
NAME ____________________
DATE __________ PER _____
“Applications Involving Right Triangles”
angle of
elevation
line of sight
Angle of Elevation: an angle measured above the line of sight
Angle of Depression: an angle measured below the line of sight
angle of
depression
EX1] From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree
is 64.3 . Find the height of the tree to the nearest foot.
EX2] From a 60 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?
EX3] An observer notes that the angle of elevation from point A to the top of a space shuttle is 27.2 .
From a point 17.5 meters further from the space shuttle, the angle of elevation is 23.9 .
Find the height of the space shuttle.
Review:
1. Complete the table below. (Try not looking at your notes!)
sin 

cos
tan 
csc 
sec 
cot 
0 , 0

30 ,
6
45 ,

4

60 ,
3

90 ,
2
2.
Find a coterminal angle for:
a)
7
3
b)
29
6
3. Find the EXACT value of the 6 trig functions of the angle  given in the figure.
 
7
6
cos  __________
sec  __________
sin   __________
csc  __________
tan   __________
cot   __________
4. What if you’re not on the Unit Circle?
of the angle  given in the figure.
Find the EXACT value of the 6 trig functions
cos  __________
sec  __________
sin   __________
csc  __________
tan   __________
cot   __________
15
7

Advanced Algebra with Trigonometry
NAME ____________________
Ch 5: “Trigonometric Functions”
DATE __________ PER _____
HOMEWORK
“Applications Involving Right Triangles”
1) Television screens are measured by the length of the diagonal of the screen. Find the width of a
19-inch television screen if the diagonal makes an angle of 38 with the base of the screen.
2) The angle of elevation from a point 116 meters from the base of the Eiffel Tower to the top of the
tower is 68.9 . Find the approximate height of the tower.
3) Venus rotates in a nearly circular orbit around the sun. The largest angle formed by Venus, Earth,
and the sun is 46.5 . The distance from Earth to the sun is approximately 149,000,000
kilometers. What is the orbital radius r of Venus? Round the answer to the nearest million
kilometers.
4) From a point 300 feet from the base of a Roman aqueduct in southern France, the angle of elevation
to the top of the aqueduct is 78 . Find the height of the aqueduct.
#5 Let  be an acute angle of a right triangle for which cot  
a) Find sin  .
24
.
7
b) Find sec  .
#6-10
Find the EXACT value of each expression.
__________ 6) sin 45  cos 60
__________ 7) csc 60 sin 30  cot 45
__________ 8) csc

6
 cos

3
__________ 9) cos
5
5
 sin
6
3
__________ 10) sin
11
7
 tan
6
4
#11-12 Convert radians to degrees or degrees to radians.
__________ 11) 200
__________ 12)
7
12