Power line pole

From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.

Correct result:

h =  11.5669 m

Solution:

$$\begin{gathered} c=30\text{ m } \\ A=18^{\circ } \\ B=10^{\circ } \\ {t}_0=\tan A^{\circ }=\tan 18^{\circ }=0.32492 \\ {t}_1=\tan B^{\circ }=\tan 10^{\circ }=0.176327=0.17633 \\ h\mathrm{/}x=\tan A=t_0 \\ h\mathrm{/}(x+c)=\tan B=t_1 \\ x=h\mathrm{/}{t}_0 \\ h\mathrm{/}(h\mathrm{/}{t}_0+c)=t_1 \\ h=t_1\cdot (h\mathrm{/}{t}_0+c) \\ h=t_1\mathrm{/}{t}_0\cdot h+c\cdot t_1 \\ h(1-t_1\mathrm{/}{t}_0)=c\cdot t_1 \\ h={\displaystyle \frac{c\cdot t_1}{1-t_1\mathrm{/}{t}_0}}={\displaystyle \frac{30\cdot 0.1763}{1-0.1763\mathrm{/}0.3249}}=11.5669\text{ m} \end{gathered}$$

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