Tower + pole

On the horizontal plane, there is a vertical tower with a flag pole on its top. At a point 9 m away from the foot if the tower, the angle of elevation of the top and bottom of the flag pole are 60°and 30° respectively. Find the height of the flag pole.

Correct answer:

h =  10.3923 m

Step-by-step explanation:

$$\begin{gathered} x=9\text{m} \\ \alpha =60°=60 \\ \beta =30°=30 \\ \tan \alpha =(h+y):x \\ \tan \beta =y:x \\ \tan \alpha =(h+x\cdot \tan \beta ):x \\ x\cdot \tan \alpha =h+x\cdot \tan \beta \\ h=x\cdot \tan \alpha -x\cdot \tan \beta \\ h=x\cdot (\tan \alpha -\tan \beta ) \\ h=x\cdot (\tan \alpha -\tan \beta )=x\cdot (\tan 60°-\tan 30°)=9\cdot (\tan 60°-\tan 30°)=9\cdot (1.732051-0.57735)=10.392=10.3923\text{m} \end{gathered}$$

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