Geometry

Solving Triangles

Cosine Rule

         

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

Details and assumptions

aa, bb and cc are the lengths of the sides opposite to the vertices AA, BB and CC, respectively.

In a triangle, an angle of 6060^\circ is formed by two sides of lengths 44 and 1111. If the length of the remaining side is a\sqrt{a}, what is aa?

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

Let ABCABC be a triangle such that A=30\angle A = 30^{\circ} , a=93 a = 9 \sqrt{3} and c=183 c = 18 \sqrt{3} . What is the value of bb?

Details and assumptions

aa, bb and cc are the lengths of the sides opposite to the vertices AA, BB and CC, respectively.

If triangle ABCABC has A=45 \angle A = 45^{\circ}, b=28b=28 and c=6+142c=\sqrt{6}+14\sqrt{2}, what is the value of a2a^2?

Details and assumptions

aa, bb and cc are the lengths of the sides opposite to the vertices AA, BB and CC, respectively.

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