Resources tagged with: Sine rule & cosine rule

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There are 16 results

Broad Topics > Pythagoras and Trigonometry > Sine rule & cosine rule

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. . . .

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 ?

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.

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.

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?

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. . . .

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?

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?

Darts and Kites

Age 14 to 16
Challenge Level

Explore the geometry of these dart and kite shapes!

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?

Raising the Roof

Age 14 to 16
Challenge Level

How far should the roof overhang to shade windows from the mid-day sun?

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?

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.

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.

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?

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.