Two ladders, of lengths 12 m and 8 m, lean against buildings on opposite sides of an
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Two ladders, of lengths 12 m and 8 m, lean against buildings on opposite sides of an alley, as shown in Figure 2.38. Show that the heights x and y (in metres) reached by the tops of the ladders in the positions shown satisfy the equations
Show that x satisfies the equation
and that the width of the alley is given by √(122 – x02), where x0 is the positive root of this equation. By first tabulating the polynomial over a suitable domain and then drawing its graph, estimate the value of x0 and the width of the alley. Check your solution of the quartic (to 2dp) using a suitable software package.
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