Redwood High School. Dpt. of Mathematics really REALLY Hard Workers' Name:________________________________
Honors Advanced Algebra 2015-16 Test S2 #7
Provide an appropriate response.
1) Without using the law of
cosines, explain why it is
impossible to construct a
triangle with lengths 8.6
cm, 11.5 cm, and 21.6 cm.
Determine the number of triangles with the given parts.
9) a = 3, b = 9, c = 11
9)
1)
10) a = 10, c = 7,
Solve.
2) What happens if C = 90°
when the law of cosines is
applied in the form
c2 = a2 + b2 - 2ab cos C?
2)
3) Given the SSS parts of a
triangle, is it better to use
the law of sines or the law
of cosines as the first step
in solving the triangle?
Explain.
3)
4) Given the ASA parts of a
triangle, is it better to use
the law of sines or the law
of cosines as the first step
in solving the triangle?
Explain.
4)
5) Given the SAS parts of a
triangle, is it better to use
the law of sines or the law
of cosines as the first step
in solving the triangle?
Explain.
5)
= 24°
11) To find the distance AB
across a river, a distance
BC of 591 m is laid off on
one side of the river. It is
found that B = 104.4° and
C = 14.9°. Find AB.
11)
12) A boat leaves the dock
and sails in a direction of
70°. Once reaching its
destination on the
opposite shore, it sails in a
direction of 272° and
docks 150 km north of its
original starting position.
What is the total distance
the boat has traveled?
12)
The given measurements may or may not determine a
triangle. If not, then state that no triangle is formed. If a
triangle is formed, then use the Law of Sines to solve the
triangle, if it is possible, or state that the Law of Sines
cannot be used.
13) B = 110°, c = 6, b = 9
13)
14) C = -3°, a = 49, c = 21
Decide whether a triangle can be formed with the given
side lengths. If so, use Heron's formula to find the area of
the triangle.
6) a = 240
6)
b = 120
c = 237
7) a = 19.0
b = 15.9
c = 13.2
7)
8) a = 29
b = 18.2
c = 8.8
8)
10)
14)
Solve the triangle. If there is more than one triangle with
the given parts, give both solutions.
15) = 99.6°
15)
b = 6.32
a = 15.9
16)
1
= 30.0°
a = 18.02
b = 36.04
16)
Solve.
17) Two tracking stations are
on the equator 119 miles
apart. A weather balloon
is located on a bearing of
N 41°E from the western
station and on a bearing
of N 20°E from the eastern
station. How far is the
balloon from the western
station?
Solve the problem.
18) Two sailboats leave a
harbor in the Bahamas at
the same time. The first
sails at 24 mph in a
direction 330°. The second
sails at 31 mph in a
direction 220°. Assuming
that both boats maintain
speed and heading, after 2
hours, how far apart are
the boats?
17)
Solve.
18)
19) Two factories blow their
whistles at exactly the
same time. If a man hears
the two blasts exactly
4.3 seconds and
5.5 seconds after they are
blown and the angle
between his lines of sight
to the two factories is
56.6°, how far apart are
the factories? Give your
result to the nearest
meter. (Use the fact that
sound travels at 344
m/sec.)
19)
20) To find the distance AB
across a river, a distance
BC of 920 m is laid off on
one side of the river. It is
found that B = 114.0° and
C = 12.7°. Find AB.
Round to the nearest
meter.
20)
21) The distance from home
plate to dead center field
in Sun Devil Stadium is
403 feet. A baseball
diamond is a square with
a distance from home
plate to first base of 90
feet. How far is it from
first base to dead center
field?
21)
22) The sides of a
parallelogram are 15 ft
and 17 ft. One angle is
43° while another angle is
137°. Find the lengths of
the diagonals of the
parallelogram (to the
nearest tenth of a foot).
22)
Find the area. Round your answer to the nearest
hundredth if necessary.
23) Find the area of the
23)
triangle with the
following measurements:
A = 46°, b = 29 ft, c = 14 ft
24) Find the area of a regular
decagon (10 sides)
inscribed in a circle of
radius 6 inches.
24)
25) A regular polygon with
10 sides is circumscribed
about a circle of radius 8
inches. Find the area of
the polygon.
25)
Find the area of the triangle.
26) a = 18.5
b = 15.5
c = 16.5
27) a = 40
b = 30.7
c = 7.3
2
26)
27)
Answer Key
Testname: HADVALG S2 TEST 7 LAW OF SINES AND COSINES WKSV4
1) In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Since
8.6 + 11.5 < 21.6, it is impossible to construct a triangle with the given sides.
2) Since cos 90° = 0, the equation becomes c2 = a2 + b2, which is the Pythagorean theorem.
3) Use the law of cosines, since at least one angle must be known to use the law of sines.
4) Use the law of sines. The law of cosines cannot be used unless at least two sides are known.
5) Must use the law of cosines, since one side and its opposite angle are necessary for the law of sines.
6) 13,845.44
7) 103.63
8) No triangle is formed.
9) 1
10) 1
11) 174 m
12) 776 km
13) C = 38.8°, A = 31.2°, a 5
14) No triangle is formed.
15) No solution
16) = 90.0°, = 60.0°, c = 31.2
17) 312 miles
18) 90.5 miles
19) 1639 meters
20) 252 meters
21) 345.3 feet
22) 11.9 ft and 29.8 ft
23) 146.03 ft2
24) 180 sin 36° 105.8 square inches
25) 171.27 square inches
26) 120.58
27) No triangle is formed.
3