Powerplant chimney

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

Correct answer:

x =  313.2801 m

Step-by-step explanation:

$$\begin{gathered} h_1=7.5\text{m} \\ \alpha =76+30/60=\frac{153}{2}=76.5{}^{\circ } \\ \beta =5+50/60=\frac{35}{6}\doteq 5.8333{}^{\circ } \\ \tan \beta =h_1:v \\ v=h_1/\tan \beta =h_1/\tan 5.8333333333333°=7.5/\tan 5.8333333333333°=7.5/0.102164=73.4113\text{m} \\ \tan \alpha =h_2:v \\ {h}_2=v\cdot \tan \alpha =v\cdot \tan 76.5°=73.4113\cdot \tan 76.5°=73.4113\cdot 4.1653=305.78007\text{m} \\ x=h_1+h_2=7.5+305.7801=313.2801\text{m} \end{gathered}$$

Try another example