Powerplant chimney

From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney?

Correct result:

x =  313.2801 m

Solution:

$$\begin{gathered} h_1=7.5\text{ m } \\ \alpha =76+30\mathrm{/}60={\displaystyle \frac{153}{2}}=76.5^{\circ } \\ \beta =5+50\mathrm{/}60={\displaystyle \frac{35}{6}}\doteq 5.8333^{\circ } \\ \tan \beta =h_1:v \\ v=h_1\mathrm{/}\tan {\beta }^{\circ }=h_1\mathrm{/}\tan 5.83333333333^{\circ }=7.5\mathrm{/}\tan 5.83333333333^{\circ }=7.5\mathrm{/}0.102164=73.4113\text{ m } \\ \tan \alpha =h_2:v \\ {h}_2=v\cdot \tan {\alpha }^{\circ }=v\cdot \tan 76.5^{\circ }=73.4113\cdot \tan 76.5^{\circ }=73.4113\cdot 4.1653=305.78007\text{ m } \\ x=h_1+h_2=7.5+305.7801=313.2801\text{ m} \end{gathered}$$

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