Sine rule and cosine rule

There are 17 NRICH Mathematical resources connected to Sine rule and cosine rule

problem

Favourite

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 area enclosed by PQRS.

problem

Favourite

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 of Pythagoras' Theorem.

problem

Favourite

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?

problem

Favourite

Three by one

Age

16 to 18

Challenge level

There are many different methods to solve this geometrical problem - how many can you find?

problem

Favourite

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.

problem

Favourite

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.

problem

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?

problem

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?

problem

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?

problem

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 ?

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For younger learners

Sine rule and cosine rule

Quadarc

Pythagoras for a tetrahedron

Hexy-metry

Three by one

Cubestick

Bendy quad

Calculating with cosines

Biggest bendy

Get cross

Square world