The mast

The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?

Correct result:

h =  23.6603 m

Solution:

$$\begin{gathered} \tan (60^{\circ })=h\mathrm{/}x \\ \tan (45^{\circ })=h\mathrm{/}(x+10) \\ x=h\mathrm{/}\tan (60^{\circ })=h\cdot t_1 \\ {t}_1=1\mathrm{/}\tan 60^{\circ }=\tan \pi \mathrm{/}3=0.57735 \\ {t}_2=\tan 45^{\circ }=\tan \pi \mathrm{/}4=1 \\ {t}_2\cdot (h\cdot t_1+10)=h \\ {t}_2\cdot h\cdot t_1+10\cdot t_2=h \\ h={\displaystyle \frac{10\cdot t_2}{1-t_2\cdot t_1}}={\displaystyle \frac{10\cdot 1}{1-1\cdot 0.5774}}=23.6603\text{ m} \end{gathered}$$

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