Elevation 80869

We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39° 25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56° 42''. How tall is the tower?

Correct answer:

h =  89.3 m

Step-by-step explanation:

α=56°42=56°+6042°=56.7°=56.7 β=39°25=39°+6025°=39.4167°39.4167 a=50 m  tan α = h/x tan β = h/(x+a)  x = h / tan α  = h / t1 t1=tanα=tan56.7° =1.522355=1.52235 t2=tanβ=tan39.416666666667° =0.821897=0.8219  t2 (h/t1+a) = h t2 h/t1+a t2 = h  h=t1t2a t1 t2=1.52240.821950 1.5224 0.821989.3143 m   Verifying Solution:  x=h/t1=89.3143/1.522458.6685 m α2=π180°arctan(xh)=π180°arctan(58.668589.3143)=10567=56.7  β2=π180°arctan(x+ah)=π180°arctan(58.6685+5089.3143)=1247339.4167 

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