Power line pole

From point A, the power pole is visible at an angle of 18 degrees. From place B, which we reach if we go from place A 30m towards the pillar at an angle of 10 degrees. Find the height of the power pole.

Correct answer:

h =  11.5669 m

Step-by-step explanation:

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

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