Resources tagged with Sine rule & cosine rule similar to Square World:
Other tags that relate to Square World
Angles - points, lines and parallel lines. Sine, cosine, tangent. Similarity and congruence. Plane shapes and their properties. Mathematical reasoning & proof. Circle properties and circle theorems. Polyhedra. Sine rule & cosine rule. Pythagoras' theorem. Regular polygons and circles.There are 16 results
Broad Topics > Pythagoras and Trigonometry > Sine rule & cosine rule
Square World
Age 16 to 18 Challenge Level:
P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
Pythagoras for a Tetrahedron
Age 16 to 18 Challenge Level:
In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .
Just Touching
Age 16 to 18 Challenge Level:
Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
Get Cross
Age 14 to 16 Challenge Level:
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
30-60-90 Polypuzzle
Age 16 to 18 Challenge Level:
Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
Quadarc
Age 14 to 16 Challenge Level:
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .
Xtra
Age 14 to 18 Challenge Level:
Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
Raising the Roof
Age 14 to 16 Challenge Level:
How far should the roof overhang to shade windows from the mid-day sun?
The Dodecahedron Explained
Age 16 to 18
What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?
Hexy-metry
Age 14 to 16 Challenge Level:
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Biggest Bendy
Age 16 to 18 Challenge Level:
Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
Bendy Quad
Age 14 to 16 Challenge Level:
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Cyclic Triangles
Age 16 to 18 Challenge Level:
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
Cubestick
Age 16 to 18 Challenge Level:
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Calculating with Cosines
Age 14 to 18 Challenge Level:
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
NRICH is part of the family of activities in the Millennium Mathematics Project.