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.

Transcribed Image Text:

1 x HH + X 1 1 || y 4 12 m Figure 2.38 O O 4m and x - y = 80 8 m/ 0 O y O HHHI