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UNIT 6 : BASIC
TRIGONOMETRY WITH TRIANGLES
LESSON
3: SINE LAW HOMEWORK QUESTIONS PAGE
1 (Solutions below)
Homework
questions: (Solutions below)
C
b h b
a
A1 ( B
D A2
Homework Questions: (all measurements in cm. unless
otherwise stated. Give answers to the
nearest tenth)
1. In each of the following triangles, the side
opposite the given angle is the shorter side.
Find angles m and n in each case to the nearest tenth of a
degree..
a)
C
8 h 8
12
A m n 320 B
D E
b)
2. In each of the following, determine which
triangles have no solution, one solution or two solutions.
a)
A
7.5 10.8
B 410
b)
13.4
P R
12.3
710
Q
c)
A
3.2 6.3
B 320 C
d) 12.4
D F
460
8.5
E
e)
M 320 P
16.4 m
750
N
f) 12.4
D F
8.5
1150
E
3. Determine the side “a” in each of the
following. Decide whether there are two
solutions, one solution or no solution.
4.
Determine all possible solutions for each of the triangles below. Include a sketch.
Solutions for # 1-3:
1. In each of the following triangles, the side
opposite the given angle is the shorter side.
Find angles m and n in each case to the nearest tenth of a
degree..
a)
C
8 h 8
12
A m n 320 B
D E
Solution:
This is the SSA case with a given
acute angle.
First we calculate the height of the triangle since the shorter
side is opposite the given angle.
C
8 12
A m 320 B
C
8 12
E
127.40 320 B
C
8 h 8
12
A 52.60 127.40 320 B
D E
b)
Solution:
This is the SSA case with a given
acute angle.
First we calculate the height of the triangle since the shorter
side is opposite the given angle.
2. In each of the following, determine which
triangles have no solution, one solution or two solutions.
a)
A
7.5
h 10.8
B 410 C
D
Solution:
This is
the SSA case with the side opposite the given
acute angle being the shorter side.
First we calculate the height of the triangle.
A
7.5
h 7.5 10.8
B 410 C
D E
b)
13.4
P R
12.3
710
Q
Solution:
Since
the side opposite the given acute angle (710) is the longer side, we have the SSA case with one solution.
c)
A
c =3.2 6.3
h=3.3
B 320 C
D
Solution:
This is
the SSA case with the side opposite the given
acute angle being the shorter side.
First we calculate the height of the triangle.
d) 12.4
D F
460
8.5
E h 8.5
H
G
Solution:
This is
the SSA case with the side opposite the given
acute angle being the shorter side.
First we redraw the diagram to show both possible triangles
(DEF and DGF) and the height FH
Next we calculate the
height of the
triangle.
12.4
D F
460
8.5
E h 8.5
H
G
e)
M 320 P
16.4 m
750
N
Solution:
This is the AAS case, two angles and a side – there is
one solution.
f) 12.4
D F
8.5
1150
E
Solution:
This is
the SSA case with an obtuse angle given. The side
opposite the given angle is the larger side.
Hence
there is one solution.
3. Determine the side “a” in each of the
following. Decide whether there are two
solutions, one solution or no solution.
Solutions:
A
3.1 h 1.5
340
B a C
This is
the SSA case with < B acute; the side across from the given angle is the
shorter side. This is the ambiguous case.
First we calculate the height of the triangle since the shorter
side (1.5) is opposite the given angle.
A
13.2 8.1
h 8.1
310
B D a C
This is
the SSA case with < B acute; the side across from the given angle is the
shorter side. This is the ambiguous case
First we calculate the height of the triangle since the shorter
side (8.1) is opposite the given angle.
A
13.2 8.1
310 122.90
B a D
A
8.1 11.4
B 680 C
a
This is
the SSA case with < B acute; the side across from the given
angle is the longer side. There is one triangle only.
First we
must find a second angle. Find < C
since we know c.