IN A SOCCER STADIUM

The angle of elevation from a point C on the ground, at the centre of the goalpost is 64.75 degrees to the highest point A of the arc, directly above the centre of the Moses Madhiba Soccer Stadium in Durban. The soccer pitch is 100 metres long (PQ in the diagram) and 64 metres wide as prescribed by FIFA for World Cup rules. The length PC = 32 metres, M is the point at the centre of the pitch directly below A and C, and AC is perpendicular to PC. A camera is positioned at D, 40 metres directly below A. By scale drawing or using trigonometry find:

1. The distance AC.
2. The angle PAC.
3. The distance from D to C.

South African National School Certificate (matric) November 2010

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