1. Law of Sines
It appears that when we have SSA, we could
end up with 0, 1, or 2 triangles! Under what
circumstances will we end up with:
0 triangles
1 triangle
2 triangles

2. Law of Sines
What if B is a right angle?
0 triangles
1 triangle
2 triangles Impossible

3. Law of Sines
What if B is an obtuse angle?
0 triangles
1 triangle
2 triangles Impossible

4. Law of Sines
How does the Law of Sines give us results that are
consistent with the geometric results?

5. A cable car carries
passengers from a
point A, which is 1.2
miles from point B at
the base of a
mountain to a point P
at the top of the
mountain. The angles of elevation of P from A and B
are 21° and 65°, respectively.
a. Approximate the distance
between A and P.  1.57 mi
b. Approximate the height of
the mountain.  0.56 mi

6. A solar panel 10 feet
in width is to be
attached to to a roof
that makes an angle
of 25° with the
horizontal.
Approximate the
length d of the brace that is needed for the panel to
make an angle of 45° with the horizontal.  3.77 ft

7. A helicoptor hovers
at an altitude that is
1000 feet above a
mountain peak of
altitude 5210 feet, as
shown in the figure.
A second, taller peak
is viewed from both
the mountaintop and
the helicoptor. From
the helicoptor, the angle of depression is 43°, and from
the mountaintop, the angle of elevation is 18°.
a. Approximate the distance  836 ft
from peak to peak.
b. Approximate the altitude  5468 ft
of the taller peak.