solve the triangle ABC if a=5,b=5√3 and c= 5
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Answer:
First, though, here's a diagram.
enter image source here
The formula for the Law of Cosine's is the following:
cos
A
=
b
2
+
c
2
−
a
2
2
b
c
cos
A
=
8
2
+
12
2
−
5
2
2
×
8
×
12
cos
A
=
0.953125
A
=
cos
−
1
(
0.953125
)
A
≈
17.61
˚
or
0.39
radians
Now for angle B:
cos
B
=
a
2
+
c
2
−
b
2
2
a
c
cos
B
=
5
2
+
12
2
−
8
2
2
×
5
×
12
cos
B
=
0.875
B
=
cos
−
1
(
0.875
)
B
≈
28.96
˚
or
0.51
radians
Finally for angle C:
cos
C
=
a
2
+
b
2
−
c
2
2
a
b
cos
C
=
5
2
+
8
2
−
12
2
2
×
5
×
8
cos
C
=
−
0.6875
C
=
cos
−
1
(
−
0.6875
)
C
=
133.43
˚
or
2.33
radians
Step-by-step explanation:
just change the values
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