The tower

From a window 8 m above the horizontal plane, the top of a tower can be seen at an elevation angle of 53°20′, and its base at a depression angle of 14°15′. How high is the tower?

Final Answer:

h =  50.3119 m

Step-by-step explanation:

$$\begin{gathered} h_1=8\text{m} \\ \alpha =53°20^{\prime }=53°+\frac{20}{60}°=53.3333°\doteq 53.3333 \\ \beta =14°15^{\prime }=14°+\frac{15}{60}°=14.25°=14.25 \\ \tan \beta =h_1:x \\ x=\frac{h_1}{\tan \beta }=\frac{h_1}{\tan 14.25°}=\frac{8}{\tan 14.25°}=\frac{8}{0.253968}=31.50008\text{m} \\ \tan \alpha =h_2:x \\ {h}_2=x\cdot \tan \alpha =x\cdot \tan 53.333333333333°=31.5001\cdot \tan 53.333333333333°=31.5001\cdot 1.343233=42.31194\text{m} \\ h=h_1+h_2=8+42.3119=50.3119\text{m} \end{gathered}$$

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