# Two vertical poles AB=15m and CD=10m are standing apart on a horizontal ground with the points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is: Option: 1 20/3 Option: 2 5 Option: 3 10/3 Option: 4 6

$\\\tan \theta=\frac{10}{\mathrm{x}}=\frac{\mathrm{h}}{\mathrm{x}_{2}} \Rightarrow \mathrm{x}_{2}=\frac{\mathrm{hx}}{10} \\ \tan \phi=\frac{15}{\mathrm{x}}=\frac{\mathrm{h}}{\mathrm{x}_{1}} \Rightarrow \mathrm{x}_{1}=\frac{\mathrm{hx}}{15} \\ \text { Now, } \mathrm{x}_{1}+\mathrm{x}_{2}=\mathrm{x}=\frac{\mathrm{hx}}{15}+\frac{\mathrm{hx}}{10} \\ \Rightarrow 1=\frac{\mathrm{h}}{10}+\frac{\mathrm{h}}{15} \Rightarrow \mathrm{h}=6$

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