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Law of Cosines: Solving for a Side>
Law of Cosines: Solving for a SideLaw of Cosines: Solving for a Side
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Question 1 of 3
1. Question
Find `CB`
Round your answer to `1` decimal place- `CB=` (4.8)`cm`
Hint
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Correct!
Incorrect
Cosine Law
$$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$where:
`a` is the side opposite angle `A`
`b` is the side opposite angle `B`
`c` is the side opposite angle `C`When to use the Cosine Law (for non-right angled triangles)
a) Given 3 sides to find an angleorb) Given 2 sides and 1 angle to find the other sideSince `2` sides are given together with an angle between them, use the Cosine Law.First, label the triangle according to the Cosine Law.
Substitute the three known values to the Cosine Law to find the length of side `CB` or `a`.From labelling the triangle, we know that the known values are those with labels `A, b` and `c`.`A=42°``b=7 cm``c=6 cm`$$\color{#007DDC}{a}^2$$ `=` $$\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$ $$\color{#007DDC}{a}^2$$ `=` $$\color{#00880A}{7}^2+\color{#9a00c7}{6}^2-2(\color{#00880A}{7})(\color{#9a00c7}{6})\cos\color{#007DDC}{42°}$$ Substitute the values `a^2` `=` `49+36-84cos42°` Simplify `a^2` `=` `85-84` `cos42°` Evaluate `cos` `42` on your calculator `a^2` `=` `85-84``(0.7431448)` Simplify `a^2` `=` `85-62.42416` `a^2` `=` `22.57583` `sqrt(a^2)` `=` `sqrt22.57583` Take the square root of both sides `a` `=` `4.75` `a` or `CB` `=` `4.8 cm` Round off to `1` decimal place 
`4.8 cm` -
Question 2 of 3
2. Question
Find `AC`
Round your answer to `1` decimal place- `AC=` (17.2)`m`
Hint
Help VideoCorrect
Great Work!
Incorrect
Cosine Law
$$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$where:
`a` is the side opposite angle `A`
`b` is the side opposite angle `B`
`c` is the side opposite angle `C`When to use the Cosine Law (for non-right angled triangles)
a) Given 3 sides to find an angleorb) Given 2 sides and 1 angle to find the other sideSince `2` sides are given together with an angle between them, use the Cosine Law.First, label the triangle according to the Cosine Law.
Substitute the three known values to the Cosine Law to find the length of side `AC` or `b`.From labelling the triangle, we know that the known values are those with labels `B, a` and `c`.`B=117°``a=12 m``c=8 m`$$\color{#007DDC}{a}^2$$ `=` $$\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$ $$\color{#00880A}{b}^2$$ `=` $$\color{#007DDC}{a}^2+\color{#9a00c7}{c}^2-2\color{#007DDC}{a}\color{#9a00c7}{c}\cos\color{#00880A}{B}$$ Rewrite formula according to given values $$\color{#00880A}{b}^2$$ `=` $$\color{#007DDC}{12}^2+\color{#9a00c7}{8}^2-2(\color{#007DDC}{12})(\color{#9a00c7}{8})\cos\color{#00880A}{117°}$$ Substitute the values `b^2` `=` `144+64-192``cos117°` Evaluate `cos` `117` on your calculator `b^2` `=` `208-192``(-0.45399)` `b^2` `=` `208+87.16676` `b^2` `=` `295.166` `sqrt(b^2)` `=` `sqrt295.166` Take the square root of both sides `b` `=` `17.18` `b` or `AC` `=` `17.2 m` Round off to `1` decimal place 
`17.2 m` -
Question 3 of 3
3. Question
Find `AB`
Round your answer to `1` decimal place- `AB=` (79.1)`m`
Hint
Help VideoCorrect
Fantastic!
Incorrect
Cosine Law
$$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$where:
`a` is the side opposite angle `A`
`b` is the side opposite angle `B`
`c` is the side opposite angle `C`When to use the Cosine Law (for non-right angled triangles)
a) Given 3 sides to find an angleorb) Given 2 sides and 1 angle to find the other sideSince `2` sides are given together with an angle between them, use the Cosine Law.First, label the triangle according to the Cosine Law.
Substitute the three known values to the Cosine Law to find the length of side `AB` or `c`.From labelling the triangle, we know that the known values are those with labels `C, a` and `b`.`C=139°``a=31 m``b=53 m`$$\color{#007DDC}{a}^2$$ `=` $$\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$ $$\color{#9a00c7}{c}^2$$ `=` $$\color{#007DDC}{a}^2+\color{#00880A}{b}^2-2\color{#007DDC}{a}\color{#00880A}{b}\cos\color{#9a00c7}{C}$$ Rewrite formula according to given values $$\color{#9a00c7}{c}^2$$ `=` $$\color{#007DDC}{31}^2+\color{#00880A}{53}^2-2\color{#007DDC}{31}\color{#00880A}{53}\cos\color{#9a00c7}{139°}$$ Substitute the values `c^2` `=` `961+2809-1643``cos139°` Evaluate `cos` `139` on your calculator `c^2` `=` `3770-1643``(-0.7547096)` `c^2` `=` `3770+2479.97568` `c^2` `=` `6249.97568` `sqrt(c^2)` `=` `sqrt6249.97568` Take the square root of both sides `c` `=` `79.05679` `c` or `AB` `=` `79.1 m` Round off to `1` decimal place 
`79.1 m`
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