Review Problems
Download
Report
Transcript Review Problems
Unit 10 – Trigonometric Applications
Review Problems
PreCalculus 10-R
• Find the indicated side x. Please
round the answer to the nearest
tenth.
149.3
Review Problems
1
• Find the indicated side x if b = 6,
3.354
Review Problems
2
• Use the Law of Cosines to
determine angle θ if a = 69.19,
b = 35.97, c = 42.82.
25.97°
3
• Use the Law of Cosines to
determine side x if a = 30, c = 36
and
correct to two
decimal places.
15.44
4
• Solve triangle ABC, if a = 17,
b = 10, and
c = 23.31,
Review Problems
5
• Solve triangle ABC, if a = 71,
Review Problems
6
• Find the indicated side x if b = 6,
3.354
Review Problems
7
• Two straight roads diverge at an
angle of 30 degrees. Two cars leave
the intersection at 5:00 P.M., one
traveling at 45 mi/h, and the other at
35 mi/h. How far apart are the cars
at 5:30 P.M.
11.4 miles
Review Problems
8
• Two tugboats that are 118 ft apart
pull a barge, as shown. If the length
of one cable is 206 and the length
of the other is 227, find the angle
formed by the two cables.
31.15°
9
• A 50 foot tower is located on the side of a
mountain that is inclined 35° to the
horizontal. A guy wire is to be attached to
the top of the tower and anchored at a
point 145 feet downhill from the base of
the tower. Find the shortest length of wire
needed.
178.44 ft
10
Find the indicated power
( 1 + i ) 16
256
Review Problems
11
Find the indicated power
-1
Review Problems
12
Find the indicated power
Review Problems
13
Find the square roots of:
Review Problems
14
Find the fourth roots of:
–625 i
Review Problems
15
Solve the following equation:
Review Problems
16
Find the vector with initial point P (6, 8)
and terminal point Q (4, 4).
Review Problems
17
For vectors u = <3, 4>, v = <–1, 3>,
find u + v
u + v = <2, 7>
Review Problems
18
Given that u =<6, 3>, v =<–2, 1>,
find 7 u – 4 v
7u – 4v = <50, 17>
Review Problems
19
u = <10, –1>, v = <10, –4>, find |u – v|.
|u – v| = 3
Review Problems
20
Find the horizontal and vertical components of the
vector v, where |v| = 34,
. Write the
vector in the form
Review Problems
21
A man pushes a lawn mower with a force
of 35 lb exerted at an angle of 43 to the
ground. Find the horizontal and vertical
components of the force.
Horizontal: 25.60lb, Vertical: –23.87lb
Review Problems
22
A jet is flying through a wind that is
blowing with a speed of 56 mi/h in the
direction N 40 E. The jet has a speed of
708 mi/h in still air, and the pilot heads
the jet in the direction N 35 E. Find the
true speed of the jet.
v = 763.8 mi/h
Review Problems
23
A straight river flows east at a speed of 7 mi/h. A
boater starts at the south shore of the river and
heads in a direction a from the shore (see the
figure). The motorboat has a speed of 20 mi/h in
still water. The boater wants to arrive at a point
on the north shore of the river directly opposite
the starting point. In what direction should the
boat be headed?
a = 110°
24
Review Problems
Find:
assuming u = 4 i + j, v = i – 7 j
–33
Review Problems
25
Find the component of u along v.
u = < –9, –8 >, v = < 3, 2 >
Review Problems
26
A constant force F = < 10, 3 > moves an object
along a straight line from the point P(1, 2) to the
point Q(8, 10). Find the work done if the distance
is measured in feet and the force is measured in
pounds.
94 ft-lb
Review Problems
27
A lawn mower is pushed a distance of 120 ft
along a horizontal path by a constant force
of 20 lb. The handle of the lawn mower is
held at an angle y = 60 from the horizontal.
Find the work done.
1200.00 ft-lb
Review Problems
28
A river flows due south at 5 mi/h. A swimmer
attempting to cross the river heads due east
swimming at 3 mi/h relative to the water.
Find the true velocity of the swimmer as a
vector.
3i –5j
Review Problems
29
Sketch the triangle and then solve the triangle
(if possible) for angle A. If two solutions exist,
find both. Please round the answer to the
nearest tenth.
53.7°
Review Problems
30
Sketch the triangle and then solve the triangle
(if possible). If two solutions exist, find both.
Please round the answer to the nearest tenth.
A 58, a 4.5, b 12.8
No Solution
Review Problems
31
Sketch the triangle and then solve the triangle
(if possible). If two solutions exist, find both.
Please round the answer to the nearest tenth.
A 58, a 11.4, b 12.8
Two Solutions
B 72.2, C 49.8, c 10.27
B 107.8, C 14.2, c 3.3
Review Problems
32
Find the area of a triangle with sides of
length 9 and 13 and included angle 56°
48.499
Review Problems
33
Find the area of a triangle with sides of
length 9, 20 and 13.
44.900
Review Problems
34
Find side x if b = 9, c = 18, and
10.785
Review Problems
35
Write the complex number in trigonometric form
1 5i
5.1(cos 78.7 i sin 78.7)
Review Problems
36
Review Problems
37
Review Problems
38
Review Problems
39
Review Problems
40
Review Problems
41
Review Problems
42
Review Problems
43
Review Problems
44
Review Problems
45
Review Problems
46
Review Problems
47
Review Problems
48
Review Problems
49
True
False
Review Problems
50
False
True
Review Problems
51
Review Problems
52
Review Problems
53
Review Problems
54
Review Problems
55
Review Problems
56
Review Problems
57
Review Problems
58
Review Problems
59
Review Problems
60
Review Problems
61
Review Problems
62
63
Review Problems
1.
2.
3.
4.
5.
149.3
3.354
25.97°
15.44
c = 23.31,
11. 256
12. -1
13.
14.
15.
6.
7.
8.
9.
10.
3.354
11.4 miles
31.15°
178.44 ft
16.
17.
18. u + v = <2, 7>
19. 7u – 4v = <50, 17>
20. |u – v| = 3
Review Problems
21.
22.Horizontal: 25.60lb,
Vertical: –23.87lb
23. v = 763.8 mi/h
24. a = 110°
25. –33
26.
27. 94 ft-lb
28. 1200.00 ft-lb
29. 3i –5j
30. 53.7°
31. No Solution
32. Two Solutions
B 72.2, C 49.8, c 10.27
B 107.8, C 14.2, c 3.3
33.
34.
35.
36.
37.
38.
39.
48.499
44.900
10.785
5.1(cos 78.7 i sin 78.7)
Review Problems
40.
47.
41.
42.
48.
43.
49.
44.
45.
46.
50. True, False
Review Problems
51. False, True
52.
57.
58.
53.
59.
54.
60.
55.
61.
56.
62.
Review Problems