Trigonometric Ratios Worksheet Page 15
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221.5 Solving Problems Using the Sine Law
KEY CONCEPTS
A
• For any △ABC, the sine law states that
sin A
sin B
sin C
c
b
_____
_____
_____
a =
=
c
b
a
b
c
B
C
_____
_____
_____
=
=
a
sin A
sin B
sin C
• A side length can be determined if the corresponding opposite angle and one other
side-angle pair are known.
• A n angle measure can be determined if the corresponding opposite side and one other
side-angle pair are known.
• I f the lengths of two sides and the measure of one angle are known, the ambiguous
case is possible. Given △ABC with known side lengths a and b and known ∠A,
if a < b, there are three possibilities:
C
If a < b sin A, then no triangle is possible.
a
b
A
If a = b sin A, then only one right triangle is possible.
C
b
a
A
B
If a > b sin A, then two triangles are possible.
C
This is the ambiguous case.
a
b
1
a
2
A
B
1
B
2
978-0-07-090893-2 Mathematics for College Technology 12 Study Guide and Exercise Book • MHR 15
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