Answer:
The height of the tower is 141.74 meters.
Step-by-step explanation:
See the attached diagram.
Let the position of the tower os AB with A as the base and B is the top.
Now, angle of elevation of point B from point C is 50°, and the from point D is 40°, and hence, CD = 50 meters,
Now, from Δ ABC, [tex]\tan 50 = \frac{AB}{AC} = \frac{x}{AC}[/tex]
⇒ [tex]AC = \frac{x}{\tan 50} = 0.839x[/tex] .......... (1)
Again, from Δ ABD, [tex]\tan 40 = \frac{AB}{AD} = \frac{x}{AD}[/tex]
⇒ [tex]AD = \frac{x}{\tan 40} =1.192x[/tex] .......... (2)
Now, DC = AD - AC
⇒ 50 = 1.192x - 0.839x
⇒ 50 = 0.353x
⇒ x = 141.74 meters.
Hence, the height of the tower is 141.74 meters. (Answer)
