Download Chapter 14 Honors Algebra 2 14.9 In each triangle, is a right angle

Chapter 14
In each triangle,
is a right angle, and two sides of the right triangle are given. Find the six trig
functions of
. Leave in fraction form.
1.
2.
a = 4, b = 3
b = 5, c = 7
3.
4.
a = 12, c = 13
a = 3, b = 5
In each triangle,
is a right angle. Sketch the triangle with the given sides and angles, then find the
remaining sides (to three decimal places) and angles to one decimal place.
5.
6.
7.
8.
9.
10.
11.
12.
(
(
(
(
(
(
(
(
)
)
)
)
)
)
)
)
13.
14.
15.
16.
17.
18.
19.
Give the measure of angles to the nearest tenth of a degree and lengths to three decimals places.
20.
A ladder 32 feet long leans against the side of a building and makes an angle of
ground. How high above the ladder is the top of the ladder?
21.
km is
with the
The angle of elevation from an observer on the ground to an airplane flying to an altitude of 8.3
. How far is the observer in a straight line from the plane?
22.
A support wire runs from the top of a utility pole that is 17 m tall to a point on the ground that is
11 m from the base of the pole. What angle does the wire make with the ground?
23.
The angle of depression from a ship to a wreck on the ocean floor is
. If the depth of the
ocean at the wreck is 156 m, how far should the ship sail so that it is directly over the wreck?
Honors Algebra 2
14.9
Chapter 15
For
find the indicated length to the nearest tenth.
( )
1.
( )
5.
For
( )
√
3.
2.
( )
4.
( )
6.
( )
find the indicated angle to the nearest tenth.
7.
( )
8.
9.
( )
10.
( )
( )
Solve each triangle. Give measurements to the nearest unit of length and the nearest degree.
11.
13.
15.
( )
( )
12.
( )
14.
( )
16.
Give the lengths to 3 decimal places and each degree to the nearest tenth.
17.
How far apart are the outer ends of the hour and minute hand of a clock at two o’clock if the
hour hand is 8 cm long and the minute hand is 15 cm long?
18.
Two ships leave from the same point at the same time on courses of
km/hr and 17 km/hr, respectively. How far apart are the ships after 1 hr?
apart at speeds of 12
19.
Two adjacent sides of a parallelogram form an acute angle and have lengths of 25 cm and 32
cm, respectively. If the shorter diagonal of the parallelogram has length 10 cm, what is the measure of
the angle between the sides?
20.
The rear windshield wiper of length 31 cm sweeps out an angle of
two outermost corners of the area swept out?
. How far apart are the
21.
A tunnel is dug from point A to point B. The distances from A to B to a third point C are 300 m
and 280 m, respectively, and (
)
. What is the distance between A and B?
Honors Algebra 2
15.7
Chapter 15
Solve each triangle. Give measurements to the nearest unit of length and the nearest degree.
1.
( )
( )
( )
3.
2.
( )
( )
( )
4.
5.
( )
( )
6.
( )
7.
( )
( )
8.
( )
10.
( )
( )
9.
Find the area of the triangle(s).
( )
11.
( )
13.
15.
12.
( )
14.
( )
( )
16.
(For problems 15 and 16 use the Law of Sines to find
( )
( ).
Give the lengths to 3 decimal places and each degree to the nearest tenth.
17.
Find the area of a parallelogram with adjacent sides of length 20 cm and 15 cm and with the
angle of measure
included between the sides.
18.
Each of two observers on the ground 15 km apart spots a plane as it passes over the line joining
the two observers. The angles of elevation of the observers’ lines of sight are
and
,
respectively. How far is the plane from the second observer at this moment?
19.
Mr. Lowery starts out hiking from a camp at point A on a course
from the line through A
and a town at point B 12 km away. He heads for a ridge at point C intending to change the direction
there and head for the town, but when he arrives at C he dings that the trail marker saying “10 km to
town B” has fallen down. By what angle should he now turn in order to head straight to B?
20.
A clock pendulum swings through an angle of
. If the distance between the two extreme
positions of the bob at the end of the shaft is 9 cm, how long is the shaft?
21.
of
One side of a parallelogram has length 40 cm. An adjacent side of length 22 cm makes an angle
with one the diagonals of the parallelogram. What is length of the diagonal?
Honors Algebra 2
15.8
Chapter 14
Express each degree measure as a radian measure using .
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Find each radian measure as a degree measure.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Evaluate using exact values from the unit circle.
21.
 
sin   
 2
22.
sec
24.
csc 3
25.
27.
csc
5
3
28.
tan
30.
cot 330o
31.
33.
sec 60o
36.
sin 315o
39.
cos 765o
42.
arcsin
45.
arcos
48.
cos (cos-1

√
Honors Algebra 2
√


4
4
3
23.
cot
 3 
cos   
 4 
26.
 11 
sec  
 6 
7
6
29.
cot
csc135o
32.
tan 270o
34.
cos180o
35.
csc210o
37.
cot 0o
38.
sec 480
40.
 15 
cos  
 6 
41.
cot
43.
cos-1
44.
tan-1 (
46.
sin-1 0
47.
arctan 1
49.
tan-1(sin 90
50.
sin(arctan √
√

2


17
4
√
)
14.2
Chapter 14
Sketch the angle whose terminal side in standard position passes through the given point, and find the
six trig functions of . Leave answers in fraction form.
1.
(
6.
(
)
)
2.
(
7.
(
)
)
For problems 11-18, find the six trig functions of
3.
(
8.
(
; III
12.
14.
; II
15.
; IV
18.
;I
√
; II
Find the six trig functions of if (
intersects the unit circle and and
)
(
4.
9.
(
) 5.
(
) 10.
(
)
)
in the given quadrant. Leave answers in fraction form.
11.
17.
)
; III
13.
;I
√
16.
) is the point where the terminal side of
satisfy the given conditions.
19.
20.
21.
22.
; IV
in standard position
√
Evaluate the trigonometric function, by drawing a triangle in the first quadrant.
23.
tan(arcsin )
Honors Math 3
24.
cos(tan-1 )
14.3
Chapter 14
For given angles, find the measure of the reference angle you would use to evaluate each function.
Then, sketch the graph showing the original angle and the reference angle , then evaluate the
function using a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
In problems 29-36 determine the measure of such that satisfies the given conditions
. Give your answer in degrees and minutes to the nearest 10’ or in decimal degrees to the nearest
tenth of a degree.
29.
;
30.
;
31.
;
32.
33.
;
34.
;
36.
;
35.
;
;
For problems 37-48 determine the measure of angle such that the terminal side of passes through
the given point and
. Give your answer in degrees to the nearest tenth, and in radians.
37.
38.
39.
41.
42.
43.
45.
46.
Honors Math 3
√
47.
√
√
40.
√
44.
√
48.
√
14.5
Chapter 14
For each of the following:
A.
State the amplitude of each function.
B.
State the maximum and minimum values.
C.
Graph the values from
.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Honors Math 3
14.6
Chapter 14
Sketch the graph of the given function over the interval
Otherwise, graph the function over the interval
if it’s fundamental period
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
.
Graph each pair of functions on one set of axes over the given interval.
13.
;
;
15.
;
;
17.
;
;
18.
;
;
14.
;
16.
;
;
;
Graph each of the following over the given interval.
19.
20.
21.
22.
23.
24.
Honors Math 3
14.7