Sine, cosine, tangent

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

What is an AC voltage? How much power does an AC power source supply?

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?

Describe how to construct three circles which have areas in the ratio 1:2:3.