Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 8
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43Figure T18 Two solutions
Figure T19 No solutions
Figure T20 One solution
Figure T21 One solution
Example: Solve ∆ABC where a = 10, c = 15 and A = 43°.
Solution: We attempt to solve for angle C by the Law of Sines:
15
10
=
°
sin
C
sin
43
so
⋅
°
15
sin
43
=
=
sin
C
. 1
023
.
10
There is no angle C for which sin C = 1.023. Hence, there is no triangle having these
sides and angles.
Example: Solve ∆ABC where a = 8.4, c = 10.5 and A = 53.13°.
Solution: By the Law of Sines,
⋅
°
10
5 .
8
4 .
10
5 .
sin
53
.
13
=
=
=
so
sin
C
. 1
000
(rounded).
sin
C
sin
53
.
13
8
4 .
Hence C = 90°. Thus, in this case there is exactly one solution. To complete the
solution, we find
=
°
−
+
=
°
−
°
=
°
B
180
(
A
C
)
180
(
143
.
13
)
36
.
87
.
Finally, solve for b by the Law of Sines:
°
b
10
5 .
10
5 .
sin
36
.
87
=
=
=
so
b
. 6
30
.
°
°
°
sin
36
.
87
sin
90
sin
90
- 8 -
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