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
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• Find the indicated side x if b = 6,
3.354
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• 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,
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• Solve triangle ABC, if a = 71,
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• Find the indicated side x if b = 6,
3.354
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• 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
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• 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
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Find the indicated power
-1
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Find the indicated power
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Find the square roots of:
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Find the fourth roots of:
–625 i
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Solve the following equation:
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Find the vector with initial point P (6, 8)
and terminal point Q (4, 4).
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For vectors u = <3, 4>, v = <–1, 3>,
find u + v
u + v = <2, 7>
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Given that u =<6, 3>, v =<–2, 1>,
find 7 u – 4 v
7u – 4v = <50, 17>
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u = <10, –1>, v = <10, –4>, find |u – v|.
|u – v| = 3
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Find the horizontal and vertical components of the
vector v, where |v| = 34,
. Write the
vector in the form
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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
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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
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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
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Find:
assuming u = 4 i + j, v = i – 7 j
–33
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Find the component of u along v.
u = < –9, –8 >, v = < 3, 2 >
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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
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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
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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
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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°
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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
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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
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Find the area of a triangle with sides of
length 9 and 13 and included angle 56°
48.499
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Find the area of a triangle with sides of
length 9, 20 and 13.
44.900
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Find side x if b = 9, c = 18, and
10.785
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Write the complex number in trigonometric form
1 5i
5.1(cos 78.7  i sin 78.7)
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True
False
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False
True
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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
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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)
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47.
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48.
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50. True, False
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51. False, True
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57.
58.
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56.
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