Test Objectives
• Demonstrate the ability to solve oblique triangles (SSA)
Law of Sines Ambiguous Case Practice Test:

#1:

Instructions: Solve each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}A=94°, c=16 \hspace{.1em}\text{m}, a=16 \hspace{.1em}\text{m}$$

$$b)\hspace{.1em}A=147°, c=25 \hspace{.1em}\text{mi}, a=4 \hspace{.1em}\hspace{.1em}\text{mi}$$

#2:

Instructions: Solve each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}B=46°, a=50 \hspace{.1em}\text{km}, b=47 \hspace{.1em}\text{km}$$

$$b)\hspace{.1em}B=114°, a=44 \hspace{.1em}\text{in}, b=78\hspace{.1em}\text{in}$$

#3:

Instructions: Solve each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}C=77°, b=49 \hspace{.1em}\text{cm}, c=6 \hspace{.1em}\text{cm}$$

$$b)\hspace{.1em}A=45°, c=44 \hspace{.1em}\text{mi}, a=34\hspace{.1em}\text{mi}$$

#4:

Instructions: Solve each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}A=82°, c=46 \hspace{.1em}\text{m}, a=5\hspace{.1em}\text{m}$$

$$b)\hspace{.1em}C=27°, b=44 \hspace{.1em}\text{in}, c=32 \hspace{.1em}\text{in}$$

#5:

Instructions: Solve each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}C=149°, b=40 \hspace{.1em}\text{ft}, c=47 \hspace{.1em}\text{ft}$$

$$b)\hspace{.1em}B=121°, a=21 \hspace{.1em}\text{ft}, b=34 \hspace{.1em}\text{ft}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\text{Not a Triangle}$$

$$b)\hspace{.1em}\text{Not a Triangle}$$

#2:

Solutions:

$$a)\hspace{.1em}C=84.1°, A=49.9°, c=65 \hspace{.1em}\text{km}$$ $$\text{or}$$ $$C=3.9°, A=130.1°, c=4.4 \hspace{.1em}\text{km}$$

$$b)\hspace{.1em}C=35°, A=31°, c=49 \hspace{.1em}\text{in}$$

#3:

Solutions:

$$a)\hspace{.1em}\text{Not a Triangle}$$

$$b)\hspace{.1em}B=68.8°, C=66.2°, b=44.8 \hspace{.1em}\text{mi}$$ $$\text{or}$$ $$B=21.2°, C=113.8°, b=17.4 \hspace{.1em}\text{mi}$$

#4:

Solutions:

$$a)\hspace{.1em}\text{Not a Triangle}$$

$$b)\hspace{.1em}A=114.4°, B=38.6°, a=64.2 \hspace{.1em}\text{in}$$ $$\text{or}$$ $$A=11.6°, B=141.4°, a=14.2 \hspace{.1em}\text{in}$$

#5:

Solutions:

$$a)\hspace{.1em}B=26°, A=5°, a=8 \hspace{.1em}\text{ft}$$

$$b)\hspace{.1em}C=27°, A=32°, c=18 \hspace{.1em}\text{ft}$$