Pythagoras

Are the two shorter sides perpendicular? Justify your answer.

Ayton is due east of Beeville.

Is Ceebury due north of Beeville? Give a reason for your answer.

A wooden beam is used to support a wall built on horizontal ground as shown in the diagram.

The edge of the beam, AB, is 8 metres long.
C is at the foot of the wall.
A is 7 metres from C.
B is 4 metres from C.
Determine whether the wall is perpendicular to the ground.
Justify your answer.

Calculate the length of its space diagonal AH, correct to 3 significant figures.

Chris wants to store his umbrella in a locker.
The locker is a cuboid with internal dimensions of length 40 centimetres, breadth 40 centimetres and height 70 centimetres.

The umbrella is 85 cm long.
He thinks it will fit into the locker from corner P to corner M.
Is he correct? Justify your answer.

The diagram below shows a circle, centre C.

The radius of the circle is 15 centimetres.
A is the mid-point of chord PQ.
The length of AB is 27 centimetres.
Calculate the length of PQ.

The diagram below shows the circular cross-section of a milk tank.

The radius of the circle, centre O, is 1.2 metres.
The width of the surface of the milk in the tank, represented by ML in the diagram, is 1.8 metres.
Calculate the depth of the milk in the tank.

Two identical shapes are used to form a logo.
Each shape is part of a circle.
The circles have centres $\displaystyle C_1$ and $\displaystyle C_2.$
The radius of each circle is 14 cm.
The logo has half-turn symmetry about the mid-point of AB.
AB is 48 cm long.

Calculate the height of the logo.

The shape below is part of a circle, centre O.

The circle has radius 13 centimetres.
AB is a chord of length 20 centimetres.
Calculate the width of the shape.

The diagram shows a cuboid, ABCDEFGH.

• The length of the cuboid, EH, is 24 centimetres.
• The breadth of the cuboid, HG, is 6 centimetres.
• The height of the cuboid, CG, is 8 centimetres.
Calculate the length of EC, the space diagonal of the cuboid.

Alan buys some identical paving slabs to make a path.
Each slab is part of a circle.

The diagram below shows a single slab.

The circle, centre C, has a radius of 50 centimetres.
Length AB is 60 centimetres.
Calculate the width of the paving slab.

Karen buys a door-number sign for her house.
The sign consists of parts of two identical circles.

AB is a chord to both circles.

• AB has length 15 centimetres.
• The radius AC has length 10 centimetres.
Calculate the width of the sign.