Trigonometry - Sine and cosine rules
Key Stage: 4 ★★★
Four rods are arranged to form a convex quadrilateral and hinged at the vertices. What possible shapes can the quadrilateral take?
This problem involves the interpretation of a very simple concrete structure, a linkage of 4 rods, and the angles that the quadrilateral formed by the rods could make. Experimental evidence will offer ideas which then need justification and proof by forming convincing arguments. The solution uses the cosine and sine rules. To find the constraints on the angles in the general case requires an argument using inequalities.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
Key Stage: 4 ★★★
Four rods are arranged to form a convex quadrilateral and hinged at the vertices. What possible shapes can the quadrilateral take?
This problem involves the interpretation of a very simple concrete structure, a linkage of 4 rods, and the angles that the quadrilateral formed by the rods could make. Experimental evidence will offer ideas which then need justification and proof by forming convincing arguments. The solution uses the cosine and sine rules. To find the constraints on the angles in the general case requires an argument using inequalities.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
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Another nice maths problem from N-rich. Complete with teacher notes, hints for the pupils and the solutions already written out for you, all you have to do is introduce the investigation to your pupils and follow the instructions. Looks at a variety of different topics including sine and cosine rules, inequalities and angles in quadrilaterals.
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