Sine, cosine, tangent

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Can you prove this formula for finding the area of a quadrilateral from its diagonals?

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

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?

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?

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

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?