Two men 2

Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45°, respectively. If the height of the tower is 50 m, find the distance between the two men.

Final Answer:

x =  136.6025 m

Step-by-step explanation:

$$\begin{gathered} h=50\text{m} \\ \alpha =30{}^{\circ } \\ \beta =45{}^{\circ } \\ \tan \alpha =h:x_1 \\ \tan \beta =h:x_2 \\ {x}_1=\frac{h}{\tan \alpha }=\frac{h}{\tan 30°}=\frac{50}{\tan 30°}=\frac{50}{0.57735}=86.60254\text{m} \\ {x}_2=\frac{h}{\tan \beta }=\frac{h}{\tan 45°}=\frac{50}{\tan 45°}=\frac{50}{1}=50\text{m} \\ x=x_1+x_2=86.6025+50=136.6025\text{m} \end{gathered}$$

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