# 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 =  313.28 m

#### Solution:

$h_{1}=7.5 \ \text{m} \ \\ α=76 + 30/60=\dfrac{ 153 }{ 2 }=76.5 \ ^\circ \ \\ β=5 + 50/60=\dfrac{ 35 }{ 6 } \doteq 5.8333 \ ^\circ \ \\ \ \\ \tan β=h_{1} : v \ \\ \ \\ v=h_{1} / \tan β ^\circ =h_{1} / \tan 5.8333333333333^\circ \ =7.5 / \tan 5.8333333333333^\circ \ =7.5 / 0.102164=73.4113 \ \\ \ \\ \tan α=h_{2} : v \ \\ \ \\ h_{2}=v \cdot \ \tan α ^\circ =v \cdot \ \tan 76.5^\circ \ =73.411298988727 \cdot \ \tan 76.5^\circ \ =73.411298988727 \cdot \ 4.1653=305.78007 \ \\ x=h_{1}+h_{2}=7.5+305.7801=313.28 \ \text{m}$

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