A construction

A construction worker is trying to find the height of a skyrise building. He is standing some distance away from the base with an elevation angle of 65 degrees. The worker moves 50 feet closer and measures the angle of elevation to be 75 degrees. Find the height of the building.

Correct answer:

h =  252.0689 ft

Step-by-step explanation:

$$\begin{gathered} \alpha =65{}^{\circ } \\ \beta =75{}^{\circ } \\ d=50\text{ft} \\ \tan \beta =h:x \\ \tan \alpha =h:t=h:(x+d) \\ h=x\cdot \tan \beta \\ h=(x+d)\cdot \tan \alpha \\ x\cdot \tan \beta =(x+d)\cdot \tan \alpha \\ x\cdot \tan \beta =x\cdot \tan \alpha +d\cdot \tan \alpha \\ x\cdot \tan \beta -x\cdot \tan \alpha =d\cdot \tan \alpha \\ x=d\cdot \frac{\tan \alpha }{\tan \beta -\tan \alpha }=d\cdot \frac{\tan 65°}{\tan 75°-\tan 65°}=50\cdot \frac{\tan 65°}{\tan 75°-\tan 65°}=50\cdot \frac{2.144507}{3.732051-2.144507}=67.54166\text{ft} \\ h=x\cdot \tan \beta =x\cdot \tan 75°=67.5417\cdot \tan 75°=67.5417\cdot 3.732051=252.069=252.0689\text{ft} \end{gathered}$$

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