Two Trees
Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
Similar triangles
This is solved by using similar triangles leading to a quartic equation which has to be solved by numerical methods. Sue Liu of Madras College used similar triangles and then the Newton Raphson to give a numerical solution. 
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Why do this problem?
It calls for constructing your own equation from the information given and then solving it by a numerical method (e.g.interval halving or the Newton Raphson method.)
Key question
When solving an equation $f(a) = 0$ can we find values of $a$ for which the function is positive and values for which the function is negative?