Test Objectives
  • Demonstrate the ability to solve oblique triangles (SAS) using the law of cosines
  • Demonstrate the ability to solve oblique triangles (SSS) using the law of cosines
  • Demonstrate the ability to find the area of a triangle using Heron's formula
Law of Cosines & Heron's Formula Practice Test:

#1:

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

$$a)\hspace{.1em}a=17 \hspace{.1em}\text{ft}, B=112°, c=26 \hspace{.1em}\text{ft}$$ Triangle ABC, a=17 ft, B=112°, c=26 ft

$$b)\hspace{.1em}b=23 \hspace{.1em}\text{cm}, C=100°, a=24 \hspace{.1em}\text{cm}$$ Triangle ABC, b=23 cm, C=100°, a=24 cm


#2:

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

$$a)\hspace{.1em}a=18 \hspace{.1em}\text{mi}, c=17 \hspace{.1em}\text{mi}, b=30 \hspace{.1em}\text{mi}$$ a=18 mi, c=17 mi, b=30 mi

$$b)\hspace{.1em}a=25 \hspace{.1em}\text{ft}, c=27 \hspace{.1em}\text{ft}, b=28 \hspace{.1em}\text{ft}$$ a=25 ft, c=27 ft, b=28 ft


#3:

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

$$a)\hspace{.1em}a=19 \hspace{.1em}\text{yd}, B=130°, c=14 \hspace{.1em}\text{yd}$$ a=19 yd, B=130°, c=14 yd

$$b)\hspace{.1em}a=11 \hspace{.1em}\text{cm}, c=17 \hspace{.1em}\text{cm}, b=10 \hspace{.1em}\text{cm}$$ a=11cm, c=17 cm, b=10 \hspace{.1em}\text{cm}


#4:

Instructions: Find the area using Heron's formula. Round your answer to the nearest tenth.

$$a)\hspace{.1em}a=9 \hspace{.1em}\text{m}, c=15 \hspace{.1em}\text{m}, b=16 \hspace{.1em}\text{m}$$ a=9 m, c=15 m, b=16 m

$$b)\hspace{.1em}a=14 \hspace{.1em}\text{cm}, c=13 \hspace{.1em}\text{cm}, b=16 \hspace{.1em}\text{cm}$$ a=14 cm, c=13 cm, b=16 cm


#5:

Instructions: Find the area using Heron's formula. Round your answer to the nearest tenth.

$$a)\hspace{.1em}b=6.8 \hspace{.1em}\text{in}, C=120°, a=5 \hspace{.1em}\text{in}$$ b=6.8 in, C=120°, a=5 in

$$b)\hspace{.1em}a=15 \hspace{.1em}\text{mi}, B=78°, c=12 \hspace{.1em}\text{mi}$$ a=15 mi, B=78°, c=12 mi


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}C=42°, A=26°, b=36 \hspace{.1em}\text{ft}$$

$$b)\hspace{.1em}A=41°, B=39°, c=36 \hspace{.1em}\text{cm}$$


#2:

Solutions:

$$a)\hspace{.1em}C=30°, A=32°, B=118°$$

$$b)\hspace{.1em}C=61°, A=54°, B=65°$$


#3:

Solutions:

$$a)\hspace{.1em}C=21°, A=29°, b=30 \hspace{.1em}\text{yd}$$

$$b)\hspace{.1em}A=38°, B=34°, C=108°$$


#4:

Solutions:

$$a)\hspace{.1em}66.3 \hspace{.1em}\text{m}^2$$

$$b)\hspace{.1em}86.8 \hspace{.1em}\text{cm}^2$$


#5:

Solutions:

$$a)\hspace{.1em}14.7 \hspace{.1em}\text{in}^2$$

$$b)\hspace{.1em}88 \hspace{.1em}\text{mi}^2$$