Cutting corners

The diagram below shows a triangle \(ABC\). The line \(CE\) is perpendicular to \(AB\) and the line \(AD\) is perpedicular to \(BC\).
The side \(AC\) is 6.5cm long and the lines \(CE\) and \(AD\) are 5.6cm and 6.0cm respectively.
How long are the other two sides of the triangle?

Show answer

Equal side and angle

In the diagram shown, the lengths \(AD = CD\) and the angles \(ABD=CBD\).
Prove that the lengths \(AB=BC\).

Show answer


Prove that \(\arctan(1)+\arctan(2)+\arctan(3)=\pi\).

Show answer & extension


A sine curve can be created with five people by giving the following instructions to the five people:
A. Stand on the spot.
B. Walk around A in a circle, holding this string to keep you the same distance away.
C. Stay in line with B, staying on this line.
D. Walk in a straight line perpendicular to C's line.
E. Stay in line with C and D. E will trace the path of a sine curve as shown here:
What instructions could you give to five people to trace a cos(ine) curve?
What instructions could you give to five people to trace a tan(gent) curve?

Show answer & extension

arccos + arcsin

What is the value of \(\arccos(x) + \arcsin(x)\)?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


palindromes sport partitions dates coins differentiation angles books shapes cryptic crossnumbers pascal's triangle square numbers colouring chess quadratics taxicab geometry irreducible numbers wordplay money factorials addition perimeter probability shape sums geometry chocolate surds symmetry lines prime numbers integration proportion complex numbers functions menace unit fractions speed logic rugby dodecagons sum to infinity floors routes trigonometry multiplication cryptic clues grids folding tube maps arrows doubling square roots dice triangles percentages algebra advent means time calculus 2d shapes bases perfect numbers multiples ave rectangles regular shapes cube numbers polygons planes star numbers coordinates triangle numbers scales integers remainders christmas graphs sequences fractions people maths spheres clocks chalkdust crossnumber division number odd numbers factors 3d shapes crosswords balancing hexagons numbers parabolas volume games digits circles crossnumbers ellipses averages area cards squares mean indices probabilty


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019