Cosine Rule Practice Problems Online

If triangle $ABC$ has side lengths $a=7$ , $b=12$ and $c=11$ , the value of $\cos A$ can be expressed as $\frac{p}{q}$ , where $p$ and $q$ are coprime positive integers. What is the value of $p+q$ ?

Details and assumptions

$a$ , $b$ and $c$ are the lengths of the sides opposite to the vertices $A$ , $B$ and $C$ , respectively.

In a triangle, an angle of $60^\circ$ is formed by two sides of lengths $4$ and $11$ . If the length of the remaining side is $\sqrt{a}$ , what is $a$ ?

If parallelogram $ABCD$ has $\overline{AB}=8$ , $\overline{BC}=4$ and $\angle ABC=60^{\circ}$ , what is the square of the length of the diagonal $\overline{BD}$ ?

Let $ABC$ be a triangle such that $\angle A = 30^{\circ}$ , $a = 9 \sqrt{3}$ and $c = 18 \sqrt{3}$ . What is the value of $b$ ?

Details and assumptions

$a$ , $b$ and $c$ are the lengths of the sides opposite to the vertices $A$ , $B$ and $C$ , respectively.

If triangle $ABC$ has $\angle A = 45^{\circ}$ , $b=28$ and $c=\sqrt{6}+14\sqrt{2}$ , what is the value of $a^2$ ?

Details and assumptions

$a$ , $b$ and $c$ are the lengths of the sides opposite to the vertices $A$ , $B$ and $C$ , respectively.

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Cosine Rule

Solving Triangles

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Cosine Rule