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

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Solving Triangles

Concept Quizzes

Challenge Quizzes

Cosine Rule

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.