### 13.5 Ambiguous Case 0, 1, or 2

```13.5 Law of Sines
Determine whether the following will have
0, 1 or 2 triangles.
Remember your rules for when you need
to check!!! (one angle and two sides)
1.)
a = 36in, b = 45in ,
<A = 22°
2.) <B = 47°, b = 12ft ,
c = 17ft
3.) <C = 23°, <B = 41°,
b = 5m
4.) a = 345 yds,
b = 201 yds, <B = 37°
5.) a = 49 miles,
b = 43 miles, <A = 63°
6.) <C = 54°, b = 85 ft,
c = 72 ft
7.) <B = 45°, c = 20mm ,
b = 16mm
8.) a = 2 in , b = 3in ,
<A = 37°
Determine
whether the
following have 0, 1, or 2
triangles…then SOLVE!

Hint: They should look familiar…
9.) a = 36 in, b = 45in ,
<A = 22°
Triangle 1:
Triangle 2:
<B = 27.9°
<B = 152.1°
<C = 116.1°
<C = 5.9°
c = 86.3in
c = 9.9in
10.) <C = 23°,
<B = 41°, b = 5m
<A = 116°
a = 6.8m
c = 3.0 m
11.) <C = 54°, b = 85 ft,
c = 72 ft
Triangle 1:
Triangle 2:
<B = 72.8°
<B = 107.2°
<A = 53.2°
<A = 18.8°
a = 71.3 ft
a = 28.7 ft
12.) a = 49 miles,
b = 43 miles, <A = 63°
<B = 51.4°
<C = 65.6°
c = 50.1 miles
13.) <B = 45°,
c = 20mm , b = 16mm