Test Objectives
  • Demonstrate the ability to apply the law of sines (SAA)
  • Demonstrate the ability to apply the law of sines (ASA)
  • Demonstrate the ability to find the area of a triangle (SAS)
Law of Sines Practice Test:

#1:

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

$$a)\hspace{.1em}A=54°, C=69°, b=27 \hspace{.1em}\text{in}$$

$$b)\hspace{.1em}B=78°, C=66°, b=15 \hspace{.1em}\text{ft}$$


#2:

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

$$a)\hspace{.1em}B=40°, C=17°, a=43 \hspace{.1em}\text{yd}$$

$$b)\hspace{.1em}A=30°, B=89°, c=21 \hspace{.1em}\text{yd}$$


#3:

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

$$a)\hspace{.1em}A=38°, C=108°, c=34 \hspace{.1em}\text{km}$$

$$b)\hspace{.1em}A=61°, B=30°, c=24 \hspace{.1em}\text{km}$$


#4:

Instructions: Find the area of each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}a=12.2\text{mi}, B=67°, c=13.7\text{mi}$$Triangle ABC

$$b)\hspace{.1em}a=7\text{cm}, C=33°, b=13.3\text{cm}$$Triangle ABC


#5:

Instructions: Find the area of each triangle ABC. Round your answers to the nearest tenth.

$$a)\hspace{.1em}c=5\text{yd}, A=25°, C=76°$$Triangle ABC

$$b) \hspace{.1em}a=8\text{m}, B=74°, A=56°$$Triangle ABC


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}c=30.1 \text{in}, B=57°, a=26 \text{in}$$ solving the triangle ABC using the law of sines

$$b)\hspace{.1em}c=14 \text{ft}, A=36°, a=9\text{ft}$$ solving the triangle ABC using the law of sines


#2:

Solutions:

$$a)\hspace{.1em}c=15 \text{yd}, A=123°, b=33 \text{yd}$$ solving the triangle ABC using the law of sines

$$b)\hspace{.1em}b=24 \text{yd}, C=61°, a=12 \text{yd}$$ solving the triangle ABC using the law of sines


#3:

Solutions:

$$a)\hspace{.1em}a=22\text{km}, B=34°, b=20\text{km}$$ solving the triangle ABC using the law of sines

$$b)\hspace{.1em}a=21\text{km}, C=89°, b=12\text{km}$$ solving the triangle ABC using the law of sines


#4:

Solutions:

$$a)\hspace{.1em}76.9 \text{mi}^{2}$$

$$b)\hspace{.1em}25.4 \text{cm}^{2}$$


#5:

Solutions:

$$a)\hspace{.1em}5.4 \text{yd}^{2}$$

$$b)\hspace{.1em}28.5 \text{m}^{2}$$