LAW OF SINES
The law of sines provides a direct approach to
the solution of oblique triangles, avoiding the necessity
of subdividing into right triangles. Let the
triangle in figure 19-21 (A) represent any
oblique triangle with all of its angles acute.
The labels used in figure 19-21 are standardized. The small letter a is used
for the side opposite angle A; small b is
opposite angle B; small c is opposite angle
C.
Figure 19-20.-(A) Oblique triangle with all angles acute; (B)
obtuse triangle.
Figure 19-21.-(A) Acute oblique triangle with standard labels; (B)
obtuse triangle with standard labels.
The law of sines states that in any triangle, whether
it is acute as in figure 19-21 (A) or obtuse
as in figure 19-21 (B), the following is true:
EXAMPLE: In figure 19-21 (A), let angle A-be 15°
and let angle C be 85°. If BC is 20 units, find
the length of AB.
SOLUTION: By the law of sines,
**
** |