ii
Math 113 - Test 3B
Name
April 10,2012
Calculators are allowed on this norlion o f the test. The 4"x 6" formula card is allowed. No other books, notes, scratch
paper are allowed. Give a complete solution to each problem and show all work. Partial credit will be given! All necessary
steps must be shown to receive full credit.
1.
(4 pts)
Solve the triangle. Round the side lengths to the nearest tenth and the angles to the nearest degree.
2.
(7 p t ~ Determine
)
whether the g i k n measurements produce onikangle, two triangles, or no triangles at
all. Solve any resulting triangles. Round the side lengths to the nearest tenth and the angles to the
nearest degree. B = 32O, a = 42, 'and b = 30
Check one:
One triangle
JTwo
triangles
No triangle
3.
Determine whether the given measurements produce one triangle, two triangles, or no triangles at
all. Solve any resulting triangles. Round the side lengths to the nearest tenth and the angles to the
nearest degree. A = 65', a = 5, and b = 69
Check one:
One triangle
Two triangles
J NO triangle
(5 pts)
j
)
h to the nearest tenth.
4. (a p t ~ Find
5.
(7 P ~ S Solve
)
the triangle.
Round the side lengths to the nearest tenth and the angles to the nearest,degree.
a=66, b=25, c = 4 5
A = 1340
-3 s 11."
a=&
& h b 2 4- cZ
LC =
z
2 7
z
2s + q s
-
Z(ZS)(YC)
~Ohb
b = LS
= 139'
7-
c=
--
-Z L ~ C , , ~ ~ ~
c = LL5
LL
3-137~
=
c=
180°- 1 3 9-14'
~
%
2
31-R
= 27"
6.
(5 pts)
7.
(8 pts)
Find the area of the triangle. Round your answer to the nearest hundredth of a square meter.
A plane leaves airport A and travels 560 miles to airport B at a bearing ofN32'E . The plane
leaves airport B and travels to airport C 320 miles away at a bearing ofS 729E . Find the distance fiom
airport A to airport C. Round your answer to the nearest mile.
t
8.
9.
( 5 pts) Plot
(6 pfi,
and label the given points in the polar coordinate system.
(
For the point 3 , - and find other polar c o o r d t e s ( r ,6 ) of the pint for which:
(a)r > 0 , - 2 n I B < O
r=3
=@
;
4
10. (6pts)Thepolar coordinates of each point are given. Find the rectangular coordinates for each point.
1 1. (6 pts) The rectangular coordinates of each point are given. Find the polar coordinates for each point.
12. (6 pts) Plot the complex number in the complex plane and write it in polar form. Express the argument in demees
,
and rouhd to 2 decimals if needed. Hint - remember the "default"for writing a number in polar form.
13. (5 pts) Write the complex number in polar form. Express the argument in degrees.
z= 2 - 2 i h
14.(s pts) Write the complex number in rectangular form.
15. (7 pts) Put z and w in polar form and find the product, zw . Leave your answer in polar form.
z
16. (6 pts) Find the quotient, - . Leave your answer in polar form.
W
"1
w = l 2 ( c o s ~ + i s i n16- -
17. (6 pts) Write the expression in standard form, a + bi .
( A+ i r