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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Pythagoras' Theorem & Trigonometry

### Tilted Squares

### Garden Shed

### Where Is the Dot?

### Compare Areas

### The Spider and the Fly

### Semi-detached

### Where to Land

### Inscribed in a Circle

### Hexy-metry

### Ladder and Cube

### Bendy Quad

### Far Horizon

### Three by One

### Cubestick

### Pythagoras' Theorem and Trigonometry - Short Problems

Y*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*

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Age 11 to 14

Challenge Level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Age 11 to 14

Challenge Level

Can you minimise the amount of wood needed to build the roof of my garden shed?

Age 14 to 16

Challenge Level

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

Age 14 to 16

Challenge Level

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Age 14 to 16

Challenge Level

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Age 14 to 16

Challenge Level

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

Age 14 to 16

Challenge Level

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

Age 14 to 16

Challenge Level

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

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?

Age 14 to 16

Challenge Level

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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.

Age 14 to 16

Challenge Level

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Age 16 to 18

Challenge Level

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

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.

Age 11 to 16

A collection of short problems on Pythagoras's Theorem and Trigonometry.

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