Math-180-Exam #5 (Chapter 7)
Practice Questions
Name___________________________________
Instructions: Show all work neatly. Answers without support will receive no credit. Your answers will be evaluated on
the correctness, completeness and use of mathematical concepts we have covered. Box your final answer and write your
answers in the answer column when possible.
Solve the triangle.
1)
1)
80°
7
55°
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle,
two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures
to the nearest degree.
2) B = 39°, b = 4, a = 22
2)
3) C = 35°, a = 18.7, c = 16.1
3)
Solve the problem.
4) To find the distance AB across a river, a distance BC of 160 m is laid off on one side of the
river. It is found that B = 109.3° and C = 15.8°. Find AB. Round to the nearest meter.
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
5)
9
4)
5)
6
5
Solve the problem.
6) Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 23 mph in a
direction 330°. The second sails at 30 mph in a direction 210°. Assuming that both boats
maintain speed and heading, after 2 hours, how far apart are the boats?
7) Let vector u have initial point P1 = (0, 2) and terminal point P2 = (3, 0). Let vector v have
initial point Q1 = (3, 0) and terminal point Q2 = (6, -2). u and v have the same direction.
Find u and v . Is u = v?
1
6)
7)
Let v be the vector from initial point P1 to terminal point P2 . Write v in terms of i and j.
8) P1 = (6, 4); P2 = (-5, -4)
Find the specified vector or scalar.
9) u = -7i - 3j, v = -5i + 7j; Find u + v.
8)
9)
10) u = -7i + 1j and v = 8i + 1j; Find u + v .
10)
Find the unit vector that has the same direction as the vector v.
11) v = -3i + j
Write the vector v in terms of i and j whose magnitude v and direction angle
12) v = 10, = 120°
11)
are given.
Solve the problem.
13) The magnitude and direction of two forces acting on an object are 35 pounds, N45°E, and
55 pounds, S30°E, respectively. Find the magnitude, to the nearest hundredth of a pound,
and the direction angle, to the nearest tenth of a degree, of the resultant force.
12)
13)
Use the given vectors to find the specified scalar.
14) u = 11i + 4j and v = -6i - 5j; Find u · v.
14)
Find the angle between the given vectors. Round to the nearest tenth of a degree.
15) u = -3i + 6j, v = 5i + 2j
15)
Use the dot product to determine whether the vectors are parallel, orthogonal, or neither.
16) v = 2i + j, w = i - 2j
16)
17) v = 3i - j, w = 6i - 2j
Find projwv =
17)
u·v
v
v 2
18) v = 2i + 3j; w = 8i - 6j
18)
2
Answer Key
Testname: MATH-180-E5-PRACTICE
1) B = 45°, a = 8.11, c = 9.75
2) no triangle
3) A1 = 42°, B1 = 103°, b1 = 27.4;
A2 = 138°, B2 = 7°, b2 = 3.4
4) 53 meters
5) A = 109°, B = 39°, C = 32°
6) 92.1 miles
7) u = 13, v = 13; yes
8) v = -11i - 8j
9) -12i + 4j
10) 5
1
-3
i+
j
11) u =
10
10
12) v = -5i + 5 3j
13) F = 57.04; = -23.6°
14) -86
15) 94.8°
16) orthogonal
17) parallel
1
(4i - 3j)
18) 25
3